168 research outputs found
A Labelling Scheme for Higher Dimensional Simplex Equations
We present a succinct way of obtaining all possible higher dimensional
generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we
could generate the two popular three-simplex equations, namely: Zamolodchikov's
tetrahedron equation (ZTE) and Frenkel and Moore equation (FME).Comment: To appear as a Letter to the Editor in J. Phys. A:Math and Ge
Multipartite entanglement in quantum spin chains
We study the occurrence of multipartite entanglement in spin chains. We show
that certain genuine multipartite entangled states, namely W states, can be
obtained as ground states of simple XX type ferromagnetic spin chains in a
transverse magnetic field, for any number of sites. Moreover, multipartite
entanglement is proven to exist even at finite temperatures. A transition from
a product state to a multipartite entangled state occurs when decreasing the
magnetic field to a critical value. Adiabatic passage through this point can
thus lead to the generation of multipartite entanglement.Comment: 4 pages, 1 figur
Sufficiency Criterion for the Validity of the Adiabatic Approximation
We examine the quantitative condition which has been widely used as a
criterion for the adiabatic approximation but was recently found insufficient.
Our results indicate that the usual quantitative condition is sufficient for a
special class of quantum mechanical systems. For general systems, it may not be
sufficient, but it along with additional conditions is sufficient. The usual
quantitative condition and the additional conditions constitute a general
criterion for the validity of the adiabatic approximation, which is applicable
to all dimensional quantum systems. Moreover, we illustrate the use of the
general quantitative criterion in some physical models.Comment: 9 pages, no figure,appearing in PRL98(2007)15040
General formalism of Hamiltonians for realizing a prescribed evolution of a qubit
We investigate the inverse problem concerning the evolution of a qubit
system, specifically we consider how one can establish the Hamiltonians that
account for the evolution of a qubit along a prescribed path in the projected
Hilbert space. For a given path, there are infinite Hamiltonians which can
realize the same evolution. A general form of the Hamiltonians is constructed
in which one may select the desired one for implementing a prescribed
evolution. This scheme can be generalized to higher dimensional systems.Comment: 6 page
GazeauKlauder squeezed states associated with solvable quantum systems
A formalism for the construction of some classes of GazeauKlauder squeezed
states, corresponding to arbitrary solvable quantum systems with a known
discrete spectrum, are introduced. As some physical applications, the proposed
structure is applied to a few known quantum systems and then statistical
properties as well as squeezing of the obtained squeezed states are studied.
Finally, numerical results are presented.Comment: 18 pages, 12 figure
Two-State Spectral-Free Solutions of Frenkel-Moore Simplex Equation
Whilst many solutions have been found for the Quantum Yang-Baxter Equation
(QYBE), there are fewer known solutions available for its higher dimensional
generalizations: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and
Moore's simplex equation (FME). In this paper, we present families of solutions
to FME which may help us to understand more about higher dimensional
generalization of QYBE.Comment: LaTeX file. Require macros: cite.sty and subeqnarray.sty to process.
To appear in J. Phys. A: Math. and Ge
Statistical Reconstruction of Qutrits
We discuss a procedure of measurement followed by the reproduction of the
quantum state of a three-level optical system - a frequency- and spatially
degenerate two-photon field. The method of statistical estimation of the
quantum state based on solving the likelihood equation and analyzing the
statistical properties of the obtained estimates is developed. Using the root
approach of estimating quantum states, the initial two-photon state vector is
reproduced from the measured fourth moments in the field . The developed
approach applied to quantum states reconstruction is based on the amplitudes of
mutually complementary processes. Classical algorithm of statistical estimation
based on the Fisher information matrix is generalized to the case of quantum
systems obeying Bohr's complementarity principle. It has been experimentally
proved that biphoton-qutrit states can be reconstructed with the fidelity of
0.995-0.999 and higher.Comment: Submitted to Physical Review
Operator Method for Nonperturbative Calculation of the Thermodynamic Values in Quantum Statistics. Diatomic Molecular Gas
Operator method and cumulant expansion are used for nonperturbative
calculation of the partition function and the free energy in quantum
statistics. It is shown for Boltzmann diatomic molecular gas with some model
intermolecular potentials that the zeroth order approximation of the proposed
method interpolates the thermodynamic values with rather good accuracy in the
entire range of both the Hamiltonian parameters and temperature. The systematic
procedure for calculation of the corrections to the zeroth order approximation
is also considered.Comment: 22 pages, 7 Postscript figures, accepted for publication in Journal
of Physics
A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator
We construct nonlinear squeezed states of a generalized isotonic oscillator
potential. We demonstrate the non-existence of dual counterpart of nonlinear
squeezed states in this system. We investigate statistical properties exhibited
by the squeezed states, in particular Mandel's parameter, second-order
correlation function, photon number distributions and parameter in
detail. We also examine the quadrature and amplitude-squared squeezing effects.
Finally, we derive expression for the -parameterized quasi-probability
distribution function of these states. All these information about the system
are new to the literature.Comment: Accepted for publication in J. Phys. A: Math. Theo
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