517 research outputs found
Two parameter Deformed Multimode Oscillators and q-Symmetric States
Two types of the coherent states for two parameter deformed multimode
oscillator system are investigated. Moreover, two parameter deformed
algebra and deformed symmetric states are constructed.Comment: LaTeX v1.2, 14 pages with no figure
Exact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed Walks
We provide the exact generating function for semi-flexible and super-flexible
interacting partially directed walks and also analyse the solution in detail.
We demonstrate that while fully flexible walks have a collapse transition that
is second order and obeys tricritical scaling, once positive stiffness is
introduced the collapse transition becomes first order. This confirms a recent
conjecture based on numerical results. We note that the addition of an
horizontal force in either case does not affect the order of the transition. In
the opposite case where stiffness is discouraged by the energy potential
introduced, which we denote the super-flexible case, the transition also
changes, though more subtly, with the crossover exponent remaining unmoved from
the neutral case but the entropic exponents changing
Q-power function over Q-commuting variables and deformed XXX, XXZ chains
We find certain functional identities for the Gauss q-power function of a sum
of q-commuting variables. Then we use these identities to obtain two-parameter
twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian
Y(sl_2). We determine the corresponding deformed trigonometric and rational
quantum R-matrices, which then are used in the computation of deformed XXX and
XXZ Hamiltonians.Comment: LaTeX, 12 page
Quantum W-algebras and Elliptic Algebras
We define quantum W-algebras generalizing the results of Reshetikhin and the
second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated
to sl_N is an associative algebra depending on two parameters. For special
values of parameters it becomes the ordinary W-algebra of sl_N, or the
q-deformed classical W-algebra of sl_N. We construct free field realizations of
the quantum W-algebras and the screening currents. We also point out some
interesting elliptic structures arising in these algebras. In particular, we
show that the screening currents satisfy elliptic analogues of the Drinfeld
relations in U_q(n^).Comment: 26 pages, AMSLATE
dS-AdS structures in the non-commutative Minkowski spaces
We consider a family of non-commutative 4d Minkowski spaces with the
signature (1,3) and two types of spaces with the signature (2,2). The Minkowski
spaces are defined by the common reflection equation and differ in
anti-involutions. There exist two Casimir elements and the fixing of one of
them leads to non-commutative "homogeneous" spaces , , and
light-cones. We present the quasi-classical description of the Minkowski
spaces. There are three compatible Poisson structures - quadratic, linear and
canonical. The quantization of the former leads to the considered Minkowski
spaces. We introduce the horospheric generators of the Minkowski spaces. They
lead to the horospheric description of , and . The
irreducible representations of Minkowski spaces and are
constructed. We find the eigen-functions of the Klein-Gordon equation in the
terms of the horospheric generators of the Minkowski spaces. They give rise to
eigen-functions on the , , and light-cones.Comment: 31 pages, LateX, typos corrected, references adde
(p,q)-Deformations and (p,q)-Vector Coherent States of the Jaynes-Cummings Model in the Rotating Wave Approximation
Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating
wave approximation are considered. Diagonalization of the Hamiltonian is
performed exactly, leading to useful spectral decompositions of a series of
relevant operators. The latter include ladder operators acting between adjacent
energy eigenstates within two separate infinite discrete towers, except for a
singleton state. These ladder operators allow for the construction of
(p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and
exact solutions to the associated moment problem are displayed, providing new
classes of coherent states for such models. Finally, in the limit of decoupled
spin sectors, our analysis translates into (p,q)-deformations of the
supersymmetric harmonic oscillator, such that the two supersymmetric sectors
get intertwined through the action of the ladder operators as well as in the
associated coherent states.Comment: 1+25 pages, no figure
Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]
Representations of the quantum superalgebra U_q[osp(1/2)] and their relations
to the basic hypergeometric functions are investigated. We first establish
Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the
representations having no classical counterparts are incorporated. Formulae for
these Clebsch-Gordan coefficients are derived, and it is observed that they may
be expressed in terms of the -Hahn polynomials. We next investigate
representations of the quantum supergroup OSp_q(1/2) which are not well-defined
in the classical limit. Employing the universal T-matrix, the representation
matrices are obtained explicitly, and found to be related to the little
Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in
all cases. Using the Clebsch-Gordan coefficients derived here, we construct new
noncommutative spaces that are covariant under the coaction of the even
dimensional representations of the quantum supergroup OSp_q(1/2).Comment: 16 pages, no figure
Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
In the context of a two-parameter deformation of the
canonical commutation relation leading to nonzero minimal uncertainties in both
position and momentum, the harmonic oscillator spectrum and eigenvectors are
determined by using techniques of supersymmetric quantum mechanics combined
with shape invariance under parameter scaling. The resulting supersymmetric
partner Hamiltonians correspond to different masses and frequencies. The
exponential spectrum is proved to reduce to a previously found quadratic
spectrum whenever one of the parameters , vanishes, in which
case shape invariance under parameter translation occurs. In the special case
where , the oscillator Hamiltonian is shown to coincide
with that of the q-deformed oscillator with and its eigenvectors are
therefore --boson states. In the general case where , the eigenvectors are constructed as linear combinations of
--boson states by resorting to a Bargmann representation of the latter
and to -differential calculus. They are finally expressed in terms of a
-exponential and little -Jacobi polynomials.Comment: LaTeX, 24 pages, no figure, minor changes, additional references,
final version to be published in JP
Exact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface Interactions
We present the solution of a linear Restricted Solid--on--Solid (RSOS) model
in a field. Aside from the origins of this model in the context of describing
the phase boundary in a magnet, interest also comes from more recent work on
the steady state of non-equilibrium models of molecular motors. While similar
to a previously solved (non-restricted) SOS model in its physical behaviour,
mathematically the solution is more complex. Involving basic hypergeometric
functions , it introduces a new form of solution to the lexicon of
directed lattice path generating functions.Comment: 10 pages, 2 figure
The interrelation between the electronic parameters of nitrogen atom and intramolecular interactions in ammonia derivatives
The electronic parameters and intramolecular interactions in the ground and transition states of inversion of the amines H₂NXHn (XHn=CH₃, NH₂, OH, F, SiH₃, PH₂, SH, Cl) were calculated using DFT (PBE96/def2-tzvpp) method. It was established that the electronacceptor properties of the XHn substituents has a prevailing influence on the change of the electronic parameters of nitrogen atom. Its increase leads to both a decrease of the charge on the nitrogen atom and an increase of the s-character and population of nitrogen lone pair (LP). All parameters under consideration correlate with the χ- and σᵢ-constants of the XHn substituents. The correlation coefficients increase when amines that contain X atoms only from one period are considered separately. It was found that the ρ values for amines containing X atoms from the second or third period are substantially different. The changes of the donor-acceptor interaction energies, s-character and LP population cannot be probable causes for different sensitivity of the electronic parameters of amines containing X atoms from different periods to the change of electron-acceptor properties of the XHn substituents. It was established that the mentioned parameters has only a subordinated influence in comparison with the influence of electron-acceptor ability of the XHn substituents. The negative charge on the nitrogen atom decreases with the increase of s-character and LP population and also with the decrease of energies of donor-acceptor interactions which lead to the withdrawal of electron density from the nitrogen atom. The s-character and LP population increase with the decrease of energies of donor-acceptor interactions which result in the reduction of electron density on the nitrogen atom. The total positive charges of the XHn groups and hydrogen atoms at the nitrogen atom decrease with increasing the electron-acceptor ability of the XHn substituents. The representation of the electron-acceptor properties of the substituents was shown to be more valid by using the χ-constants than by using the σᵢ-constants. The chlorine atom is a weak electron acceptor in comparison with an amino group
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