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1.
Two families of coherent states (the eigenstates of the annihilation operator and the Klauder–Gazeau temporally stable coherent states) are constructed for the Legendre oscillator defined in this paper. Bibliography: 14 titles. 相似文献
2.
We define the Gegenbauer oscillator and introduce a family of Barut–Girardello coherent states (eigenstates of a relevant annihilation operator) for this oscillator. Gegenbauer (ultraspherical) polynomials play the same role for this oscillator as Hermite polynomials do in the case of the usual boson oscillator. We establish the validity of unity decomposition for the introduced states and evaluate their overlap. These results reproduce similar results obtained earlier by the authors for Legendre and Chebyshev polynomials. Bibliography: 38 titles. 相似文献
3.
Partially coherent fields (mixed states) described by correlation functions (density matrices) are considered. The lower bound
for the product of the uncertainties in the wave spatial localization and in its Fourier transform localization is obtained
as a function of the space dimensionality. For the state with minimum uncertainty, it is shown that increasing the dimensionality
leads to decreasing the phase volume corresponding to one mode in the canonical distribution of the correlation function as
compared with the phase volume in the case of a coherent field (pure state).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 427–434, December, 1998. 相似文献
4.
K. Thirulogasanthar A. Krzyżak Q. D. Katatbeh 《Theoretical and Mathematical Physics》2006,149(1):1366-1381
The quaternionic vector coherent states are realized as coherent states of the supersymmetric harmonic oscillator with broken
symmetry in analogy with the standard canonical coherent states of the ordinary harmonic oscillator. We study the nonclassical
properties of the oscillator, such as the photon number distribution and signal-to-quantum-noise ratio in terms of these states
and discuss the squeezing properties and the temporal stability of the coherent states. We obtain the orthogonal polynomials
associated with the quaternionic vector coherent states.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 80–98, October, 2006. 相似文献
5.
E. V. Damaskinski 《Journal of Mathematical Sciences》1991,54(3):894-900
A simple method based on generalized coherent states is proposed for calculation of Berry's phase. In this paper we calculate Berry's phase for a translated oscillator in standard coherent states as well as Berry's phase in squeezed states and spin coherent states, i.e., coherent states for the SU(1, 1) and SU(2) groups, respectively.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 51–59, 1988. 相似文献
6.
The Charlier polynomials are used for constructing oscillator-like systems. We introduce coherent states of the system are defined and study the main properties (in particular, the (over)completeness property). We show that the coherent states on the associated uncertainty relation take the minimum value. In the case under consideration, the Mandel parameter vanishes, which corresponds to the Poisson statistics of quasiexcitation spectrum for the considered oscillator. Bibliography: 30 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 3–15. 相似文献
7.
A new method to construct coherent states of a time-dependent forced harmonic oscillator was given. The close relation to
the classical forced oscillator and the minimum uncertainty relation were investigated. The applied periodic force (off-resonance
case), in general, will attenuate the AA phase. 相似文献
8.
S. V. Kozyrev 《Theoretical and Mathematical Physics》1997,110(2):265-266
Free coherent states for a system with two degrees of freedom are defined. It is shown that for a set of coherent states corresponding
to an eigenvalue of the annihilation operator, a 2-adic parameter naturally appears.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 334–336, February, 1997. 相似文献
9.
In certain circumstances, the uncertainty, ΔS[φ], of a quantum observable, S, can be bounded from below by a finite overall constant ΔS>0, i.e., ΔS[φ]≥ΔS, for all physical states φ. For example, a finite lower bound to the resolution of distances has been used to model a natural ultraviolet cutoff at
the Planck or string scale. In general, the minimum uncertainty of an observable can depend on the expectation value, t=〈φ,S
φ〉, through a function ΔS
t
of t, i.e., ΔS[φ]≥ΔS
t
, for all physical states φ with 〈φ,S
φ〉=t. An observable whose uncertainty is finitely bounded from below is necessarily described by an operator that is merely symmetric
rather than self-adjoint on the physical domain. Nevertheless, on larger domains, the operator possesses a family of self-adjoint
extensions. Here, we prove results on the relationship between the spacing of the eigenvalues of these self-adjoint extensions
and the function ΔS
t
. We also discuss potential applications in quantum and classical information theory.
相似文献
10.
We obtain the coherent states for a particle in the noncentral Hartmann potential by transforming the problem into four isotropic
oscillators evolving in a parametric time. We use path integration over the holomorphic coordinates to find the quantum states
for these oscillators. The decomposition of the transition amplitudes gives the coherent states and their parametric-time
evolution for the particle in the Hartmann potential. We also derive the coherent states in the parabolic coordinates by considering
the transition amplitudes between the coherent states and eigenstates in the configuration space.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 439–452, June, 2008. 相似文献
11.
V. V. Borzov 《Theoretical and Mathematical Physics》2007,153(3):1656-1670
We construct a system (a generalized oscillator) that is similar to the oscillator and is related to a system of orthogonal
polynomials on the real axis. We define coherent states in the Fock space associated with the generalized oscillator. In the
example of the generalized oscillator related to the Gegenbauer polynomials, we prove the (super)completeness of these coherent
states, i.e., we construct a measure determining a partition of unity. We present a formula that allows calculating the Mandel
parameter for the constructed coherent states.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 363–380, December, 2007. 相似文献
12.
We study the baker’s map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization
properties of eigenstates, in the semiclassical régime. Simple counterexamples show that quantum unique ergodicity fails for
this model. We obtain, however, lower bounds on the entropies associated with semiclassical measures, as well as on the Wehrl
entropies of eigenstates. The central tool of the proofs is an “entropic uncertainty principle”.
Submitted: December 21, 2005; Accepted: March 1, 2006 相似文献
13.
S. A. Polshin 《Theoretical and Mathematical Physics》1999,121(2):1473-1477
The de Sitter SO(4, 1) group conformal action is used to construct two different systems of generalized coherent states for
the de Sitter group in the three-dimensional Euclidean space. The two systems of states have the physical sense of particles
and antiparticles in the de Sitter space. The scalar product of two coherent states is a two-point function in the de Sitter
space.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121. No. 2, pp. 258–263. November, 1999. 相似文献
14.
A. V. Komlov 《Theoretical and Mathematical Physics》2007,153(3):1643-1651
We consider a Grassmannian version of the noncommutative U(1) sigma model specified by the energy functional E(P) = ‖[a, P]‖
HS
2
, where P is an orthogonal projection operator in a Hilbert space H and a: H → H is the standard annihilation operator. With
H realized as a Bargmann-Fock space, we describe all solutions with a one-dimensional range and prove that the operator [a,
P] is densely defined in H for a certain class of projection operators P with infinite-dimensional ranges and kernels.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 347–357, December, 2007. 相似文献
15.
Let 𝔄 denote the C*-algebra of bounded operators on L
2 ℝ generated by: (i) all multiplications a(M) by functions a∈C[ − ∞, + ∞], (ii) all multiplications by 2π-periodic continuous functions, and (iii) all operator of the form F
−1
b(M)F, where F denotes the Fourier transform and b∈C[ − ∞, + ∞]. A given A ∈ 𝔄 is a Fredholm operator if and only if σ(A) and γ(A) are invertible, where σ denotes the continuous extension of the usual principal symbol, while γ denotes an operator-valued “boundary principal symbol” (the “boundary” here consists of two copies of the circle, one at
each end of the real line). We give two proofs of the fact that K
0(𝔄) is isomorphic to ℤ and that K
1(𝔄) is isomorphic to ℤ ⊕ ℤ . We do it first by computing the connecting mappings in the six-term exact sequence associated
to σ. For the second proof, we show that the image of γ is isomorphic to the direct sum of two copies of the crossed product
, where α denotes the translation-by-one automorphism. Its K-theory can be computed using the Pimsner–Voiculescu exact sequence,
and that information suffices for the analysis of the standard cyclic exact sequence associated to γ.
Received: February 2006 相似文献
16.
Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials
The authors continue to study generalized coherent states for oscillator-like systems connected with a given family of orthogonal
polynomials. In this work, we consider oscillators connected with Meixner and Meixner— Pollaczek polynomials and define generalized
coherent states for these oscillators. A completeness condition for these states is proved by solution of a related classical
moment problem. The results are compared with the other authors ones. In particular, we show that the Hamiltonian of the relativistic
model of a linear harmonic oscillator can be treated as the linearization of a quadratic Hamiltonian, which arises naturally
in our formalism. Bibliography: 56 titles.
The authors dedicate this work to their friend and colleague P. P. Kulish on the occasion of his 60th birthday
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 66–93. 相似文献
17.
For n-body problems with quasihomogeneous potentials in ℝk (2[ n/2] ⩽ k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly
the circles with center at the origin and the configuration of the n-bodies is always a regular n - 1 simplex with fixed side
length. 相似文献
18.
Sh. M. Nagiyev 《Theoretical and Mathematical Physics》2018,194(2):313-327
Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass M(t) and a nonrelativistic particle with a variable mass M(t) in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field. 相似文献
19.
F. M. Mukhamedov 《Theoretical and Mathematical Physics》2000,123(1):489-493
The Ising model on a Bethe lattice of orderk≥2 is considered. For maximum or minimum translation-invariant Gibbs states of this model, the relations between the von Neumann
algebras generated by these states for the Gelfand-Neimark-Segal representation are found. These algebras can be of types
IIIλ, λ∈(0, 1), and III1.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 88–93, April, 2000. 相似文献