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1.
A. Lavagno A. M. Scarfone P. Narayana Swamy 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):351-354
On the basis of the quantum q-oscillator algebra in the
framework of quantum groups and non-commutative
q-differential calculus, we investigate a possible
q-deformation of the classical Poisson bracket in order
to extend a generalized q-deformed dynamics in the
classical regime. In this framework, classical q-deformed
kinetic equations, Kramers and Fokker-Planck equations, are
also studied. 相似文献
2.
By constructing the q-analogue of the Heisenberg-Weyl algebra in terms of usual creation and annihilation operators of boson states in the Fock space, the boson realization method recently suggested[7-11] is generalized to obtain a class of representations of quantum group in the Fock space. The q-deformed differential realization of quantum groups proposed by Alvarez-Gaume is derived by making use of the boson realization in this paper. 相似文献
3.
D. Buchholz 《Communications in Mathematical Physics》1975,42(3):269-279
Starting from the basic postulates of local relativistic quantum theory, the asymptotic incoming and outgoing collision states of massless Fermions are constructed. The corresponding Hilbert spaces have Fock structure and thus allow the usual definition of anS-matrix. In contrast to the massive case, there are geometric relations between the local nets of the underlying field algebra and the asymptotic fields. 相似文献
4.
q变形叠加态及其特性 总被引:1,自引:0,他引:1
利用q-振子代数提出了一种由q变形振子的本征态(q变形光子数态)叠回由成的态。给出了这种q有叠加态的定义,研究了它们的量子统计性质。也讨论了这种态的压缩和q压缩,并进一步研究了它们的寻常高阶压缩和q高阶压缩。q变形振子是一种非线性振子,通过这些讨论,推广通常的叠加态。 相似文献
5.
F. Büyükkiliç D. Demirhan 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(4):705-711
In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the
Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function,
the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis as well as extensive (q=1) standard thermostatistical relations of the Bose and Fermi systems are recovered.
Received 17 September 1999 相似文献
6.
We construct the algebra of the creation and destruction operators for spin 1/2 particles obeying a new exclusion principle
which is “more exclusive” than Pauli’s exclusion principle: an orbital state shall not contain more than one particle, whether
spin up or spin down. The consequences of this algebra are studied and applications to the Hubbard model in condensed matter
physics are indicated.
An erratum to this article is available at . 相似文献
7.
J. Gemmer G. Mahler 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(2):249-257
For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and
the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state
trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost
all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition
this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes'
principle. It is these states which thermodynamical systems should generically evolve into.
Received 13 June 2002 / Received in final form 14 November 2002 Published online 4 February 2003
RID="a"
ID="a"e-mail: jochen@theol.physik.uni-stuttgart.de 相似文献
8.
The method of q-deformed boson realization is extended to the caee that q is a root of unity. By using thb method, many irreducible and indecomposable representations of each su balgebra in a su balgebra chain of the quantum universal enveloping algebra (quan tum algebra) (Cl)q are obtained on the q-deformed Fock space and its quotient space. AB an example, the representations of (C3)q are constructed in explicit forms. Besides, by embedding (A1)q = (Cl)q, into the subalgebra chain, a new realisation of (A1)q and its representations are obtained. 相似文献
9.
10.
M. Bortz S. Sergeev 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(3):395-405
We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding
eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures. 相似文献
11.
A. Camacho 《General Relativity and Gravitation》2003,35(7):1153-1160
In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisenberg algebra, and hence the Hamiltonian is not anymore diagonal in the occupation number representation. Additionally, we show the changes that the energy expectation value suffers as result of the presence of an extra term in the uncertainty principle. The existence of a deformed dispersion relation is also proved. 相似文献
12.
We have constructed a new kind of two-mode bosonic realization of SU(1,1) Lie algebra, on the basis of which the SU(1,1) generalized coherent states in the two-mode Fock space are derived. These two-mode SU(1,1) coherent states, which are called uncorrelated two-mode SU(1,1) coherent states, include three special cases. For these states, we study the mean photon number distribution and their non-classical properties, which are photon anti-bunching, violations of Cauchy-Schwarz inequality and two-mode squeezing. 相似文献
13.
For a lattice system with a finite number of Fermions and spins on each lattice point, conditional expectations relative to an even product state (such as Fermion Fock vacuum) are introduced and the corresponding standard potential for any given dynamics, or more generally for any given time derivative (at time 0) of strictly local operators, is defined, with the case of the tracial state previously treated as a special case. The standard potentials of a given time derivative relative to different product states are necessarily different but they are shown to give the same set of equilibrium states, where one can compare states satisfying the variational principle (for translation invariant states) or the local thermodynamical stability or the Gibbs condition, all in terms of the standard potential relative to different even product states. 相似文献
14.
利用具有量子群对称性的q变形量子谐振子Fock态│n>q生成q变形量子谐振子的Glauber相干态(q-Glauber相干态│a>q)。还讨论了q-Glauber相干态│a>q的完备性、粒子数分布、振子强度分布和最小测不准关系,指出q-Glauber相干态│a>q的相干程度可以用q参数来描述。 相似文献
15.
A. Lavagno A.M. Scarfone P. Narayana Swamy 《The European Physical Journal C - Particles and Fields》2006,47(1):253-261
On the basis of non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate
a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears invariant under
the action of the q-symplectic group of transformations. Within this framework we introduce the q-deformed Hamilton equations
and we derive the evolution equation for some simple q-deformed mechanical systems governed by a scalar potential dependent
only on the coordinate variable. It appears that the q-deformed Hamiltonian, which is the generator of the equation of motion,
is generally not conserved in time but, in correspondence, a new constant of motion is generated. Finally, by following the
standard canonical quantization rule, we compare the well-known q-deformed Heisenberg algebra with the algebra generated by
the q-deformed Poisson bracket.
PACS 02.45.Gh, 45.20.-d, 03.65.-w, 02.20.Uw 相似文献
16.
The thermal Green functions of the quantum-mechanical harmonic oscillator are constructed within the framework of nonextensive
statistical mechanics with normalized
q
-expectation values. For the Tsallis index q greater than unity, these functions are found to be expressed analytically in terms of the Hurwitz zeta function. It is found
that influence of the nonextensivity on the time-ordered thermal propagator is relevant only at the “on-shell” states. In
particular, the finite-temperature contribution to the thermal propagator becomes enhanced for the strong nonextensivity.
Received 30 September 1998 相似文献
17.
Quantum statistical mechanics of ideal gas obeying fractional exclusion statistics: a systematic study 总被引:1,自引:0,他引:1
G. Su M. Suzuki 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):577-582
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics
are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and internal
energy, the equation of state, as well as the thermodynamic properties are thoroughly discussed. Some novel results are obtained.
Received: 23 January 1998 / Accepted: 17 March 1998 相似文献
18.
Aziz El Kaabouchi Laurent Nivanen Qiuping Alexandre Wang Jean Pierre Badiali Alain Le Méhauté 《Central European Journal of Physics》2009,7(3):549-554
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra
proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical
systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate
an algebra in which the conventional algebraic rules are generalized.
相似文献
19.
We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well. 相似文献
20.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(2):179-208
We study a general class of nonlinear mean field
Fokker-Planck equations in relation with an effective generalized
thermodynamical (E.G.T.) formalism. We show that these equations describe
several physical systems such as: chemotaxis of bacterial
populations, Bose-Einstein condensation in the canonical ensemble,
porous media, generalized Cahn-Hilliard equations, Kuramoto model,
BMF model, Burgers equation, Smoluchowski-Poisson system for
self-gravitating Brownian particles, Debye-Hückel theory of
electrolytes, two-dimensional turbulence... In particular, we show
that nonlinear mean field Fokker-Planck equations can provide
generalized Keller-Segel models for the chemotaxis of
biological populations. As an example, we introduce a new model of
chemotaxis incorporating both effects of anomalous diffusion and
exclusion principle (volume filling). Therefore, the notion of
generalized thermodynamics can have applications for concrete
physical systems. We also consider nonlinear mean field
Fokker-Planck equations in phase space and show the passage from
the generalized Kramers equation to the generalized Smoluchowski
equation in a strong friction limit. Our formalism is simple and
illustrated by several explicit examples corresponding to Boltzmann,
Tsallis, Fermi-Dirac and Bose-Einstein entropies among others. 相似文献