62 research outputs found
Boson-fermion mappings for odd systems from supercoherent states
We extend the formalism whereby boson mappings can be derived from
generalized coherent states to boson-fermion mappings for systems with an odd
number of fermions. This is accomplished by constructing supercoherent states
in terms of both complex and Grassmann variables. In addition to a known
mapping for the full so(2+1) algebra, we also uncover some other formal
mappings, together with mappings relevant to collective subspaces.Comment: 40 pages, REVTE
Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics
The Moyal product is used to cast the equation for the metric of a
non-hermitian Hamiltonian in the form of a differential equation. For
Hamiltonians of the form with polynomial this is an exact
equation. Solving this equation in perturbation theory recovers known results.
Explicit criteria for the hermiticity and positive definiteness of the metric
are formulated on the functional level.Comment: References adde
Spin in the path integral: anti-commuting versus commuting variables
We discuss the equivalence between the path integral representations of spin
dynamics for anti-commuting (Grassmann) and commuting variables and establish a
bosonization dictionary for both generators of spin and single fermion
operators. The content of this construction in terms of the representations of
the spin algebra is discussed in the path integral setting. Finally it is shown
how a `free field realization' (Dyson mapping) can be constructed in the path
integral.Comment: 9 pages, Late
Boson-fermion mapping and dynamical supersymmetry in fermion models
We show that a dynamical supersymmetry can appear in a purely fermionic
system. This ``supersymmetry without bosons" is constructed by application of a
recently introduced boson-fermion Dyson mapping from a fermion space to a space
comprised of collective bosons and ideal fermions. In some algebraic fermion
models of nuclear structure, particular Hamiltonians may lead to collective
spectra of even and odd nuclei that can be unified using the dynamical
supersymmetry concept with Pauli correlations exactly taken into account.Comment: 20 pages. Revtex. One PostScript figure available on request from P
Factored coset models: A unifying approach to different bosonization schemes
We discuss various bosonization schemes from a path integral perspective. Our
analysis shows that the existence of different bosonization schemes, such as
abelian bosonization of non-abelian models and non-abelian bosonization of
fermions with colour and flavour indices, can be understood as different ways
of factoring out a dynamically trivial coset which contains the fermions. From
this perspective follows the importance of the coset model in ensuring the
correct superselection rules on the bosonic level.Comment: 20 pages, Revte
Violation of the Nernst heat theorem in the theory of thermal Casimir force between Drude metals
We give a rigorous analytical derivation of low-temperature behavior of the
Casimir entropy in the framework of the Lifshitz formula combined with the
Drude dielectric function. An earlier result that the Casimir entropy at zero
temperature is not equal to zero and depends on the parameters of the system is
confirmed, i.e. the third law of thermodynamics (the Nernst heat theorem) is
violated. We illustrate the resolution of this thermodynamical puzzle in the
context of the surface impedance approach by several calculations of the
thermal Casimir force and entropy for both real metals and dielectrics.
Different representations for the impedances, which are equivalent for real
photons, are discussed. Finally, we argue in favor of the Leontovich boundary
condition which leads to results for the thermal Casimir force that are
consistent with thermodynamics.Comment: 24 pages, 3 figures, accepted for publication in Phys. Rev.
Thermal correction to the Casimir force, radiative heat transfer, and an experiment
The low-temperature asymptotic expressions for the Casimir interaction
between two real metals described by Leontovich surface impedance are obtained
in the framework of thermal quantum field theory. It is shown that the Casimir
entropy computed using the impedance of infrared optics vanishes in the limit
of zero temperature. By contrast, the Casimir entropy computed using the
impedance of the Drude model attains at zero temperature a positive value which
depends on the parameters of a system, i.e., the Nernst heat theorem is
violated. Thus, the impedance of infrared optics withstands the thermodynamic
test, whereas the impedance of the Drude model does not. We also perform a
phenomenological analysis of the thermal Casimir force and of the radiative
heat transfer through a vacuum gap between real metal plates. The
characterization of a metal by means of the Leontovich impedance of the Drude
model is shown to be inconsistent with experiment at separations of a few
hundred nanometers. A modification of the impedance of infrared optics is
suggested taking into account relaxation processes. The power of radiative heat
transfer predicted from this impedance is several times less than previous
predictions due to different contributions from the transverse electric
evanescent waves. The physical meaning of low frequencies in the Lifshitz
formula is discussed. It is concluded that new measurements of radiative heat
transfer are required to find out the adequate description of a metal in the
theory of electromagnetic fluctuations.Comment: 19 pages, 4 figures. svjour.cls is used, to appear in Eur. Phys. J.
Surface-impedance approach solves problems with the thermal Casimir force between real metals
The surface impedance approach to the description of the thermal Casimir
effect in the case of real metals is elaborated starting from the free energy
of oscillators. The Lifshitz formula expressed in terms of the dielectric
permittivity depending only on frequency is shown to be inapplicable in the
frequency region where a real current may arise leading to Joule heating of the
metal. The standard concept of a fluctuating electromagnetic field on such
frequencies meets difficulties when used as a model for the zero-point
oscillations or thermal photons in the thermal equilibrium inside metals.
Instead, the surface impedance permits not to consider the electromagnetic
oscillations inside the metal but taking the realistic material properties into
account by means of the effective boundary condition. An independent derivation
of the Lifshitz-type formulas for the Casimir free energy and force between two
metal plates is presented within the impedance approach. It is shown that they
are free of the contradictions with thermodynamics which are specific to the
usual Lifshitz formula for dielectrics in combination with the Drude model. We
demonstrate that in the impedance approach the zero-frequency contribution is
uniquely fixed by the form of impedance function and does not need any of the
ad hoc prescriptions intensively discussed in the recent literature. As an
example, the computations of the Casimir free energy between two gold plates
are performed at different separations and temperatures. It is argued that the
surface impedance approach lays a reliable framework for the future
measurements of the thermal Casimir force.Comment: 21 pages, 3 figures, to appear in Phys. Rev.
Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir force measurements
We report new constraints on extra-dimensional models and other physics
beyond the Standard Model based on measurements of the Casimir force between
two dissimilar metals for separations in the range 0.2--1.2 m. The Casimir
force between an Au-coated sphere and a Cu-coated plate of a
microelectromechanical torsional oscillator was measured statically with an
absolute error of 0.3 pN. In addition, the Casimir pressure between two
parallel plates was determined dynamically with an absolute error of mPa. Within the limits of experimental and theoretical errors, the results
are in agreement with a theory that takes into account the finite conductivity
and roughness of the two metals. The level of agreement between experiment and
theory was then used to set limits on the predictions of extra-dimensional
physics and thermal quantum field theory. It is shown that two theoretical
approaches to the thermal Casimir force which predict effects linear in
temperture are ruled out by these experiments. Finally, constraints on Yukawa
corrections to Newton's law of gravity are strengthened by more than an order
of magnitude in the range 56 nm to 330 nm.Comment: Revtex 4, 35 pages, 14 figures in .gif format, accepted for
publication in Phys. Rev.
Normal and Lateral Casimir Forces between Deformed Plates
The Casimir force between macroscopic bodies depends strongly on their shape
and orientation. To study this geometry dependence in the case of two deformed
metal plates, we use a path integral quantization of the electromagnetic field
which properly treats the many-body nature of the interaction, going beyond the
commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary
deformations we provide an analytical result for the deformation induced change
in Casimir energy, which is exact to second order in the deformation amplitude.
For the specific case of sinusoidally corrugated plates, we calculate both the
normal and the lateral Casimir forces. The deformation induced change in the
Casimir interaction of a flat and a corrugated plate shows an interesting
crossover as a function of the ratio of the mean platedistance H to the
corrugation length \lambda: For \lambda \ll H we find a slower decay \sim
H^{-4}, compared to the H^{-5} behavior predicted by PWS which we show to be
valid only for \lambda \gg H. The amplitude of the lateral force between two
corrugated plates which are out of registry is shown to have a maximum at an
optimal wavelength of \lambda \approx 2.5 H. With increasing H/\lambda \gtrsim
0.3 the PWS approach becomes a progressively worse description of the lateral
force due to many-body effects. These results may be of relevance for the
design and operation of novel microelectromechanical systems (MEMS) and other
nanoscale devices.Comment: 20 pages, 5 figure
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