Casimir effect

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Casimir forces on parallel plates

Casimir forces on parallel plates

File:Water wave analogue of Casimir effect.ogv

In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.

The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured, and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy. In fact "Casimir's original goal was to compute the van der Waals force between polarizable molecules" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) or virtual particles of quantum fields.

Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.

Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).

In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.

Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas exhibit the Casimir force.

Overview

The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alters the vacuum expectation value of the energy of the second quantized electromagnetic field. Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects.

Possible causes

Vacuum energy

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The vacuum has, implicitly, all of the properties that a particle may have: spin, or polarization in the case of light, energy, and so on. On average, most of these properties cancel out: the vacuum is, after all, "empty" in this sense. One important exception is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator states that the lowest possible energy or zero-point energy that such an oscillator may have is

$E=\begin{array}{c}\frac{1}{2}\end{array}\hslash \omega .$

Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable; this argument is the underpinning of the theory of renormalizationPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.. In all practical calculations, this is how the infinity is always handledPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.. In a deeper sense, however, renormalization is unsatisfyingTemplate:Why, and the removal of this infinity presents a challenge in the search for a Theory of Everything. Currently there is no compelling explanation for why this infinity should be treated as essentially zero; a non-zero value is essentially the cosmological constantPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. and any large value causes trouble in cosmology.

Relativistic van der Waals force

Alternatively, a 2005 paper by Robert Jaffe of MIT states that "Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of alpha, corresponds to the alpha → infinity limit," and that "The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates."

Effects

Casimir's observation was that the second-quantized quantum electromagnetic field, in the presence of bulk bodies such as metals or dielectrics, must obey the same boundary conditions that the classical electromagnetic field must obey. In particular, this affects the calculation of the vacuum energy in the presence of a conductor or dielectric.

Consider, for example, the calculation of the vacuum expectation value of the electromagnetic field inside a metal cavity, such as, for example, a radar cavity or a microwave waveguide. In this case, the correct way to find the zero-point energy of the field is to sum the energies of the standing waves of the cavity. To each and every possible standing wave corresponds an energy; say the energy of the nth standing wave is $E_n$. The vacuum expectation value of the energy of the electromagnetic field in the cavity is then

$⟨E⟩=\frac{1}{2}\sum _n{E}_n$

with the sum running over all possible values of n enumerating the standing waves. The factor of 1/2 corresponds to the fact that the zero-point energies are being summed (it is the same 1/2 as appears in the equation $E=\hslash \omega /2$). Written in this way, this sum is clearly divergent; however, it can be used to create finite expressions.

In particular, one may ask how the zero-point energy depends on the shape s of the cavity. Each energy level $E_n$ depends on the shape, and so one should write $E_n(s)$ for the energy level, and $⟨E(s)⟩$ for the vacuum expectation value. At this point comes an important observation: the force at point p on the wall of the cavity is equal to the change in the vacuum energy if the shape s of the wall is perturbed a little bit, say by $\delta s$, at point p. That is, one has

$F(p)=-{\frac{\delta ⟨E(s)⟩}{\delta s}|}_p.$

This value is finite in many practical calculations.

Attraction between the plates can be easily understood by focusing on the one dimensional situation. Suppose that a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). With a << L, the states within the slot of width a are highly constrained so that the energy E of any one mode is widely separated from that of the next. This is not the case in open region L, where there is a large number (about L/a) of states with energy evenly spaced between E and the next mode in the narrow slot---in other words, all slightly larger than E. Now on shortening a by da (< 0), the mode in the slot shrinks in wavelength and therefore increases in energy proportional to -da/a, whereas all the outside L/a states lengthen and correspondingly lower energy proportional to da/L (note the denominator). The net change is slightly negative, because all the L/a modes' energies are slightly larger than the single mode in the slot.

Derivation of Casimir effect assuming zeta-regularization

In the original calculation done by Casimir, he considered the space between a pair of conducting metal plates at distance $a$ apart. In this case, the standing waves are particularly easy to calculate, because the transverse component of the electric field and the normal component of the magnetic field must vanish on the surface of a conductor. Assuming the parallel plates lie in the xy-plane, the standing waves are

${\psi }_n(x,y,z;t)=e^{-i{\omega }_{n}t}{e}^{i{k}_{x}x+i{k}_{y}y}\sin \left(k_{n}z\right)$

where $\psi$ stands for the electric component of the electromagnetic field, and, for brevity, the polarization and the magnetic components are ignored here. Here, $k_x$ and $k_y$ are the wave vectors in directions parallel to the plates, and

$k_n=\frac{n\pi }{a}$

is the wave-vector perpendicular to the plates. Here, n is an integer, resulting from the requirement that ψ vanish on the metal plates. The frequency of this wave is

${\omega }_n=c\sqrt{{k_x}^2+{k_y}^2+\frac{n^2{\pi }^2}{a^2}}$

where c is the speed of light. The vacuum energy is then the sum over all possible excitation modes

$⟨E⟩=\frac{\hslash }{2}\cdot 2\int \frac{Ad{k}_{x}d{k}_y}{(2\pi {)}^2}\sum _{n=1}^{\mathrm{\infty }}{\omega }_n$

where A is the area of the metal plates, and a factor of 2 is introduced for the two possible polarizations of the wave. This expression is clearly infinite, and to proceed with the calculation, it is convenient to introduce a regulator (discussed in greater detail below). The regulator will serve to make the expression finite, and in the end will be removed. The zeta-regulated version of the energy per unit-area of the plate is

$\frac{⟨E(s)⟩}{A}=\hslash \int \frac{d{k}_{x}d{k}_y}{(2\pi {)}^2}\sum _{n=1}^{\mathrm{\infty }}{\omega }_n|{\omega }_n{|}^{-s}.$

In the end, the limit $s\to 0$ is to be taken. Here s is just a complex number, not to be confused with the shape discussed previously. This integral/sum is finite for s real and larger than 3. The sum has a pole at s = 3, but may be analytically continued to s = 0, where the expression is finite. The above expression simplifies to:

$\frac{⟨E(s)⟩}{A}=\frac{\hslash c^{1-s}}{4{\pi }^2}\sum _n{\int }_0^{\mathrm{\infty }}2\pi qdq{|q^2+\frac{{\pi }^2{n}^2}{a^2}|}^{(1-s)/2}$

where polar coordinates $q^2=k_x^2+k_y^2$ were introduced to turn the double integral into a single integral. The $q$ in front is the Jacobian, and the $2\pi$ comes from the angular integration. The integral converges if Re[s] > 3, resulting in

$\frac{⟨E(s)⟩}{A}=-\frac{\hslash c^{1-s}{\pi }^{2-s}}{2a^{3-s}}\frac{1}{3-s}\sum _n|n{|}^{3-s}.$

The sum diverges at s in the neighborhood of zero, but if the damping of large-frequency excitations corresponding to analytic continuation of the Riemann zeta function to s = 0 is assumed to make sense physically in some way, then one has

$\frac{⟨E⟩}{A}=\underset{s\to 0}{lim}\frac{⟨E(s)⟩}{A}=-\frac{\hslash c{\pi }^2}{6a^3}\zeta (-3).$

But $\zeta (-3)=1/120$ and so one obtains

$\frac{⟨E⟩}{A}=\frac{-\hslash c{\pi }^2}{3\cdot 240a^3}.$

The analytic continuation has evidently lost an additive positive infinity, somehow exactly accounting for the zero-point energy (not included above) outside the slot between the plates, but which changes upon plate movement within a closed system. The Casimir force per unit area $F_c/A$ for idealized, perfectly conducting plates with vacuum between them is

$\frac{F_c}{A}=-\frac{d}{da}\frac{⟨E⟩}{A}=-\frac{\hslash c{\pi }^2}{240a^4}$

where

$\hslash$ (hbar, ħ) is the reduced Planck constant,

$c$ is the speed of light,

$a$ is the distance between the two plates.

The force is negative, indicating that the force is attractive: by moving the two plates closer together, the energy is lowered. The presence of $\hslash$ shows that the Casimir force per unit area $F_c/A$ is very small, and that furthermore, the force is inherently of quantum-mechanical origin.

NOTE: In Casimir's original derivation [1], a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). The 0-point energy on both sides of the plate is considered. Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler-Maclaurin summation with a regularizing function (e.g., exponential regularization) not so anomalous as $|{\omega }_n{|}^{-s}$ in the above.

More recent theory

Casimir's analysis of idealized metal plates was generalized to arbitrary dielectric and realistic metal plates by Lifshitz and his students. Using this approach, complications of the bounding surfaces, such as the modifications to the Casimir force due to finite conductivity, can be calculated numerically using the tabulated complex dielectric functions of the bounding materials. Lifshitz' theory for two metal plates reduces to Casimir's idealized 1/a⁴ force law for large separations a much greater than the skin depth of the metal, and conversely reduces to the 1/a³ force law of the London dispersion force (with a coefficient called a Hamaker constant) for small a, with a more complicated dependence on a for intermediate separations determined by the dispersion of the materials.

Lifshitz' result was subsequently generalized to arbitrary multilayer planar geometries as well as to anisotropic and magnetic materials, but for several decades the calculation of Casimir forces for non-planar geometries remained limited to a few idealized cases admitting analytical solutions. For example, the force in the experimental sphere–plate geometry was computed with an approximation (due to Derjaguin) that the sphere radius R is much larger than the separation a, in which case the nearby surfaces are nearly parallel and the parallel-plate result can be adapted to obtain an approximate R/a³ force (neglecting both skin-depth and higher-order curvature effects). However, in the 2000s a number of authors developed and demonstrated a variety of numerical techniques, in many cases adapted from classical computational electromagnetics, that are capable of accurately calculating Casimir forces for arbitrary geometries and materials, from simple finite-size effects of finite plates to more complicated phenomena arising for patterned surfaces or objects of various shapes.

Measurement

One of the first experimental tests was conducted by Marcus Sparnaay at Philips in Eindhoven, in 1958, in a delicate and difficult experiment with parallel plates, obtaining results not in contradiction with the Casimir theory, but with large experimental errors. Some of the experimental details as well as some background information on how Casimir, Polder and Sparnaay arrived at this point are highlighted in a 2007 interview with Marcus Sparnaay.

The Casimir effect was measured more accurately in 1997 by Steve K. Lamoreaux of Los Alamos National Laboratory, and by Umar Mohideen and Anushree Roy of the University of California at Riverside. In practice, rather than using two parallel plates, which would require phenomenally accurate alignment to ensure they were parallel, the experiments use one plate that is flat and another plate that is a part of a sphere with a large radius.

In 2001, a group (Giacomo Bressi, Gianni Carugno, Roberto Onofrio and Giuseppe Ruoso) at the University of Padua (Italy) finally succeeded in measuring the Casimir force between parallel plates using microresonators.

Regularisation

In order to be able to perform calculations in the general case, it is convenient to introduce a regulator in the summations. This is an artificial device, used to make the sums finite so that they can be more easily manipulated, followed by the taking of a limit so as to remove the regulator.

The heat kernel or exponentially regulated sum is

$⟨E(t)⟩=\frac{1}{2}\sum _n\hslash |{\omega }_n|\exp (-t|{\omega }_n|)$

where the limit $t\to 0^{+}$ is taken in the end. The divergence of the sum is typically manifested as

$⟨E(t)⟩=\frac{C}{t^3}+\text{finite}$

for three-dimensional cavities. The infinite part of the sum is associated with the bulk constant C which does not depend on the shape of the cavity. The interesting part of the sum is the finite part, which is shape-dependent. The Gaussian regulator

$⟨E(t)⟩=\frac{1}{2}\sum _n\hslash |{\omega }_n|\exp (-t^2|{\omega }_n{|}^2)$

is better suited to numerical calculations because of its superior convergence properties, but is more difficult to use in theoretical calculations. Other, suitably smooth, regulators may be used as well. The zeta function regulator

$⟨E(s)⟩=\frac{1}{2}\sum _n\hslash |{\omega }_n||{\omega }_n{|}^{-s}$

is completely unsuited for numerical calculations, but is quite useful in theoretical calculations. In particular, divergences show up as poles in the complex s plane, with the bulk divergence at s = 4. This sum may be analytically continued past this pole, to obtain a finite part at s = 0.

Not every cavity configuration necessarily leads to a finite part (the lack of a pole at s = 0) or shape-independent infinite parts. In this case, it should be understood that additional physics has to be taken into account. In particular, at extremely large frequencies (above the plasma frequency), metals become transparent to photons (such as X-rays), and dielectrics show a frequency-dependent cutoff as well. This frequency dependence acts as a natural regulator. There are a variety of bulk effects in solid state physics, mathematically very similar to the Casimir effect, where the cutoff frequency comes into explicit play to keep expressions finite. (These are discussed in greater detail in Landau and Lifshitz, "Theory of Continuous Media".)

Generalities

The Casimir effect can also be computed using the mathematical mechanisms of functional integrals of quantum field theory, although such calculations are considerably more abstract, and thus difficult to comprehend. In addition, they can be carried out only for the simplest of geometries. However, the formalism of quantum field theory makes it clear that the vacuum expectation value summations are in a certain sense summations over so-called "virtual particles".

More interesting is the understanding that the sums over the energies of standing waves should be formally understood as sums over the eigenvalues of a Hamiltonian. This allows atomic and molecular effects, such as the van der Waals force, to be understood as a variation on the theme of the Casimir effect. Thus one considers the Hamiltonian of a system as a function of the arrangement of objects, such as atoms, in configuration space. The change in the zero-point energy as a function of changes of the configuration can be understood to result in forces acting between the objects.

In the chiral bag model of the nucleon, the Casimir energy plays an important role in showing the mass of the nucleon is independent of the bag radius. In addition, the spectral asymmetry is interpreted as a non-zero vacuum expectation value of the baryon number, cancelling the topological winding number of the pion field surrounding the nucleon.

Dynamical Casimir effect

The dynamical Casimir effect is the production of particles and energy from an accelerated moving mirror. This reaction was predicted by certain numerical solutions to quantum mechanics equations made in the 1970s. In May 2011 an announcement was made by researchers at the Chalmers University of Technology, in Gothenburg, Sweden, of the detection of the dynamical Casimir effect. In their experiment, microwave photons were generated out of the vacuum in a superconducting microwave resonator. These researchers used a modified SQUID to change the effective length of the resonator in time, mimicking a mirror moving at the required relativistic velocity. If confirmed this would be the first experimental verification of the dynamical Casimir effect.

Analogies

A similar analysis can be used to explain Hawking radiation that causes the slow "evaporation" of black holes (although this is generally visualized as the escape of one particle from a virtual particle-antiparticle pair, the other particle having been captured by the black hole).Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Constructed within the framework of quantum field theory in curved spacetime, the dynamical Casimir effect has been used to better understand acceleration radiation such as the Unruh effect.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Repulsive forces

There are few instances wherein the Casimir effect can give rise to repulsive forces between uncharged objects. Evgeny Lifshitz showed (theoretically) that in certain circumstances (most commonly involving liquids), repulsive forces can arise. This has sparked interest in applications of the Casimir effect toward the development of levitating devices. An experimental demonstration of the Casimir-based repulsion predicted by Lifshitz was recently carried out by Munday et al. Other scientists have also suggested the use of gain media to achieve a similar levitation effect, though this is controversial because these materials seem to violate fundamental causality constraints and the requirement of thermodynamic equilibrium (Kramers-Kronig relations). Casimir and Casimir-Polder repulsion can in fact occur for sufficiently anisotropic electrical bodies; for a review of the issues involved with repulsion see Milton et al.

Applications

It has been suggested that the Casimir forces have application in nanotechnology, in particular silicon integrated circuit technology based micro- and nanoelectromechanical systems, silicon array propulsion for space drives, and so-called Casimir oscillators.

On 4 June 2013 it was reported that a conglomerate of scientists from Hong Kong University of Science and Technology, University of Florida, Harvard University, Massachusetts Institute of Technology, and Oak Ridge National Laboratory have for the first time demonstrated a compact integrated silicon chip that harnesses the power of the Casimir effect.

See also

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• Casimir pressure
• Scharnhorst effect
• Stochastic electrodynamics
• Van der Waals force

References

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Further reading

Introductory readings

• Casimir effect description from University of California, Riverside's version of the Usenet physics FAQ.
• A. Lambrecht, The Casimir effect: a force from nothing, Physics World, September 2002.
• Casimir effect on Astronomy Picture of the Day

Papers, books and lectures

• H. B. G. Casimir, and D. Polder, "The Influence of Retardation on the London-van der Waals Forces", Phys. Rev. 73, 360–372 (1948).
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• S. K. Lamoreaux, "Demonstration of the Casimir Force in the 0.6 to 6 µm Range", Phys. Rev. Lett. 78, 5–8 (1997)
• M. Bordag, U. Mohideen, V.M. Mostepanenko, "New Developments in the Casimir Effect", Phys. Rep. 353, 1–205 (2001), arXiv. (200+ page review paper.)
• Kimball A.Milton: "The Casimir effect", World Scientific, Singapore 2001,ISBN 981-02-4397-9
• Diego Dalvit, et al.: Casimir Physics. Springer, Berlin 2011, ISBN 978-3-642-20287-2
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• J. D. Barrow, "Much ado about nothing", (2005) Lecture at Gresham College. (Includes discussion of French naval analogy.)
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 (Also includes discussion of French naval analogy.)
• Jonathan P. Dowling, "The Mathematics of the Casimir Effect", Math. Mag. 62, 324–331 (1989).
• Patent № PCT/RU2011/000847 Author Urmatskih.

Temperature dependence

• Measurements Recast Usual View of Elusive Force from NIST
• V.V. Nesterenko, G. Lambiase, G. Scarpetta, Calculation of the Casimir energy at zero and finite temperature: some recent results, arXiv:hep-th/0503100 v2 13 May 2005

External links

• Casimir effect article search on arxiv.org
• G. Lang, The Casimir Force web site, 2002
• J. Babb, bibliography on the Casimir Effect web site, 2009