共查询到20条相似文献,搜索用时 718 毫秒
1.
Marek Biskup Lincoln Chayes Shannon Starr 《Communications in Mathematical Physics》2007,269(3):611-657
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins satisfy . From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with . The most notable examples are the quantum orbital-compass model on and the quantum 120-degree model on which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. 相似文献
2.
Asao Arai 《Letters in Mathematical Physics》2006,77(3):283-290
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral
of a family of self-adjoint operators
acting in the Hilbert space
, where
is the Hilbert space of the quantum radiation field. The fiber operator
is called the Hamiltonian of the Dirac polaron with total momentum
. The main result of this paper is concerned with the non-relativistic (scaling) limit of
. It is proven that the non-relativistic limit of
yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. 相似文献
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6.
Local Asymptotic Normality in Quantum Statistics 总被引:1,自引:1,他引:0
The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result
from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of Gaussian state ϕ
u
of an algebra of canonical commutation relations. The convergence holds for all “local parameters” such that parametrizes a neighborhood of a fixed point .
In order to prove the result we define weak and strong convergence of quantum statistical experiments which extend to the
asymptotic framework the notion of quantum sufficiency introduces by Petz. Along the way we introduce the concept of canonical
state of a statistical experiment, and investigate the relation between the two notions of convergence. For the reader’s convenience
and completeness we review the relevant results of the classical as well as the quantum theory.
Dedicated to Slava Belavkin on the occasion of his 60th anniversary 相似文献
7.
Consider in the operator family . P
0 is the quantum harmonic oscillator with diophantine frequency vector ω, F
0 a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space, and . Then there exist independent of and an open set such that if and , the quantum normal form near P
0 converges uniformly with respect to . This yields an exact quantization formula for the eigenvalues, and for the classical Cherry theorem on convergence of Birkhoff’s normal form for complex frequencies is recovered.
Partially supported by PAPIIT-UNAM IN106106-2. 相似文献
8.
Atsushi Nakayashiki 《Letters in Mathematical Physics》2009,89(1):85-100
The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring generated by commuting derivations. A -free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models
assuming a certain conjecture. We propose another -free resolution of A by extending the construction in the classical finite dimensional integrable system associated with a certain family of hyperelliptic
curves to infinite dimension assuming a similar conjecture. The relation between the two constructions is given.
相似文献
9.
Dominique Fellah 《Letters in Mathematical Physics》2007,80(2):101-113
10.
We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra
form which we can then ‘quantise’ by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor
space , compactified Minkowski space and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local
form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the
formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we
show that the pull-back of the tautological bundle on pulls back to the basic instanton on and that this observation quantises to obtain the Connes-Landi instanton on θ-deformed S
4 as the pull-back of the tautological bundle on our θ-deformed . We likewise quantise the fibration and use it to construct the bundle on θ-deformed that maps over under the transform to the θ-deformed instanton.
The work was mainly completed while S.M. was visiting July-December 2006 at the Isaac Newton Institute, Cambridge, which both
authors thank for support. 相似文献
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H. Q. Lu L. M. Shen P. Ji G. F. Ji N. J. Sun 《International Journal of Theoretical Physics》2003,42(4):837-844
In this paper we consider the classical Euclidean wormhole solution of the Born—Infeld scalar field. The corresponding classical Euclidean wormhole solution can be obtained analytically for both very small and large
. At the extreme limit of small
the wormhole solution has the same format as one obtained by Giddings and Strominger (Nuclear Physics B
306, 890, 1988). At the extreme limit of large
the wormhole solution is a new one. The wormhole wave functions can also be obtained for both very small and large
. These wormhole wave functions are regarded as solutions of quantum-mechanical Wheeler—Dewitt equation with certain boundary conditions. 相似文献
13.
K. B. Korotchenko 《Russian Physics Journal》1990,33(9):780-783
It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold
4. A classical particle on
4 is described as a free particle (
p=0), while the quantum particle, as a free wave (
s=0).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1990. 相似文献
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15.
The spin-fermion model describes a two level quantum system
(spin 1/2) coupled to finitely many free Fermi gas reservoirs
which are in thermal equilibrium at inverse temperatures β
j
. We consider non-equilibrium initial conditions where not all β
j
are the same. It is known that, at small coupling, the combined system
has a unique non-equilibrium steady state (NESS) characterized by strictly sitive entropy production. In this paper we study
linear response in this NESS and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated
by temperature differentials.
Dedicated to Jean Michel Combes on the occasion of his sixtyfifth birthday 相似文献
16.
Approximating Multi-Dimensional Hamiltonian Flows by Billiards 总被引:2,自引:2,他引:0
The behavior of a point particle traveling with a constant speed in a region , undergoing elastic collisions at the regions’s boundary, is known as the billiard problem. Various billiard models serve
as approximation to the classical and semi-classical motion in systems with steep potentials (e.g. for studying classical
molecular dynamics, cold atom’s motion in dark optical traps and microwave dynamics). Here we develop methodologies for examining
the validity and accuracy of this approximation. We consider families of smooth potentials , that, in the limit , become singular hard-wall potentials of multi-dimensional billiards. We define auxiliary billiard domains that asymptote,
as to the original billiards, and provide, for regular trajectories, asymptotic expansion of the smooth Hamiltonian solution
in terms of these billiard approximations. The asymptotic expansion includes error estimates in the C
r
norm and an iteration scheme for improving this approximation. Applying this theory to smooth potentials that limit to the
multi-dimensional close to ellipsoidal billiards, we predict when the billiard’s separatrix splitting (which appears, for
example, in the nearly flat and nearly oblate ellipsoids) persists for various types of potentials. 相似文献
17.
Recently, A. A. Kirillov introduced an important notion of classical and quantum family algebras. Here the criterion of commutativity is given. The quantum eigenvalues of
are computed. 相似文献
18.
Sudzhit Basu 《Russian Physics Journal》1982,25(10):956-960
A unique linear rule of constructing quantum operators defined by the probability operator
for coordinates and momenta, is considered.
is assumed to be a normalized, positive definite operator, establishing a dynamical correspondence between the classical and quantum Poisson brackets. It is shown that such an operator exists in the case of a harmonic oscillator. The principal implications of the suggested rule of constructing the operators of physical quantities are determined, in comparison with the corresponding results of conventional quantum mechanics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 89–93, October, 1982. 相似文献
19.
Fluctuation spectrum in an exactly solvable model with dissipation: A new model of the Flicker noise
O. Yu. Dinariev 《Russian Physics Journal》1990,33(10):821-826
A system is considered consisting of a harmonic oscillator and a field interacting with it. A quadratic Lagrangian is used, so that the model is exactly solvable. Under some conditions, the model exhibits a dissipative behavior of a selected oscillator. A canonical transformation is found which brings the Hamiltonian to a diagonal form, which is used to compute the quantum correlation and spectral functions of the oscillator fluctuations. It is found that the model allows for a low-frequency spectrum of the form
for the driving force, and
for the oscillator coordinate (Flicker noise).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 13–18, October, 1990. 相似文献