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1.
Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators a, a
, N and the unity 1 such as [a, N] = a, [a
, N] = –a
, a
a = (N) and aa
= (N + 1). We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the e igenstates of a (or a
). We give various examples, in particular we consider functions that are linear combinations of q
N, q
–N and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations. 相似文献
2.
We study phase properties of generalized coherent states obtained from usual Fock coherent states by adapting classical methods of statistical mechanics, in particular, the well-known procedure of thermodynamical limit. Moreover, we show that there exists a close connection between these states and the states describing boson systems with condensation properties. 相似文献
3.
A class of states obtained by extremizing the energy of a system under certain conditions is introduced and their properties are compared with those of the coherent states. Conditions under which these states move without change of shape and follow the classical path are investigated. 相似文献
4.
John R. Klauder 《International Journal of Theoretical Physics》1994,33(3):509-522
The usual quantization procedures interpret canonical transformations in an active way linking them with unitary transformations, while the quantization procedure offered by coherent states completely separates classical canonical transformations and unitary operator transformations. By exploiting this property, along with a physically motivated shadow metric, it is seen how to realize the quantization process in as coordinate-free a form as holds in classical mechanics. 相似文献
5.
Mario Rasetti 《International Journal of Theoretical Physics》1975,14(1):1-21
The concept of coherent states for arbitrary Lie group is suggested as a tool for explicitly obtaining an integral representation of the partition function, whenever the Hamiltonian has a dynamical group. Two examples are thoroughly discussed: the case of the nilpotent group of Weyl related to a generic many-body problem with two-body interactions, and the case of
SU(1, 1)() relevant for a superfluid system. 相似文献
6.
A. M. Perelomov 《Communications in Mathematical Physics》1975,44(2):197-210
Properties of system of the coherent states related to representations of the class I of principal series of the motion groups of symmetric spaces of rank 1 have been studied. It has been proved that such states are given by horospherical kernels and are the generalization of the plane waves for the case of symmetric spaces. 相似文献
7.
Anatol Odzijewicz 《Communications in Mathematical Physics》1992,150(2):385-413
Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena.This work was supported in part by The Swedish Institute 相似文献
8.
D.A. Trifonov 《Physics letters. A》1974,48(3):165-166
The most general form of the minimality-preserving Hamiltonians is found and the uncertainty products ΔqΔp are calculated for some quadratic quantum systems 相似文献
9.
Coherent states via decoherence 总被引:1,自引:0,他引:1
10.
K. N. Afanasiev V. G. Volostnikov E. V. Razueva 《Bulletin of the Russian Academy of Sciences: Physics》2008,72(5):652-655
An approach has been developed with the use of coherent states for constructing wavelets based on spiral light beams. 相似文献
11.
A detailed physical characterisation of the coherent states and squeezed states of a realq-deformed oscillator is attempted. The squeezing andq-squeezing behaviours are illustrated by three different model Hamiltonians, namely i) Batemann Hamiltonian ii) harmonic oscillator
with time dependent mass and frequency and iii) a system with constant mass and time-dependent frequency. 相似文献
12.
We demonstrate coherent optical detection of highly excited Rydberg states (up to n=124) using electromagnetically induced transparency (EIT), providing a direct nondestructive probe of Rydberg energy levels. We show that the EIT spectra allow direct optical detection of electric field transients in the gas phase, and we extend measurements of the fine structure splitting of the nd series up to n=96. Coherent coupling of Rydberg states via EIT could also be used for cross-phase modulation and photon entanglement. 相似文献
13.
G. Roepstorff 《Communications in Mathematical Physics》1970,19(4):301-314
A criterion is derived for the existence of a selfadjoint and semibounded momentum operator in a non-Fock representation of the free photon field given by a coherent state. The representation of the translation group is constructed and it is shown that the rotation group, hence the homogeneous Lorentz group, cannot be unitarily implemented in the so-called infrared sectors. 相似文献
14.
Henri Moscovici 《Communications in Mathematical Physics》1977,54(1):63-68
The coherent state representations of a connected and simply connected nilpotent Lie group are characterized in terms of the Kirillov correspondence, as being those irreducible unitary representations whose associated orbits under the coadjoint representation are linear varieties. 相似文献
15.
Vyacheslav Spiridonov 《Letters in Mathematical Physics》1995,35(2):179-185
New coherent states of theq-Weyl algebraAA
–qA
A = 1,0 <q < 1, are constructed. They are defined as eigenstates of the operatorA
which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA
A d2/dx2 is used for illustrations.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia. 相似文献
16.
《Physics letters. A》2005,337(3):183-188
Coherent states of the two-dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a well-defined elliptical polarization. They are coherent correlated states with respect to the usual Cartesian position and momentum operators. A set of creation and annihilation operators is defined in polar coordinates, and it is shown that these same states are precisely coherent states with respect to such operators. 相似文献
17.
18.
Nuri ünal 《Central European Journal of Physics》2009,7(4):774-785
In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations
of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming
the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed
in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve
in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing
eigenvalues.
相似文献
19.
Misra A 《Physical review D: Particles and fields》1994,50(6):4088-4096
20.
In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to collect some recent results. We begin by recalling the basic constructions of geometric quantization in both the Kähler and non-Kähler cases. We then study the reproducing kernels associated to the quantum Hilbert spaces and use them to define symplectic coherent states. The rest of the paper is dedicated to the properties of symplectic coherent states and the corresponding Berezin–Toeplitz quantization. Specifically, we study overcompleteness, symplectic analogues of the basic properties of Bargmann’s weighted analytic function spaces, and the ‘maximally classical’ behavior of symplectic coherent states. We also find explicit formulas for symplectic coherent states on compact Riemann surfaces. 相似文献