236 research outputs found
Vacuum Structure of Two-Dimensional Theory on the Orbifold
We consider the vacuum structure of two-dimensional theory on
both in the bosonic and the supersymmetric cases. When the size
of the orbifold is varied, a phase transition occurs at , where
is the mass of . For , there is a unique vacuum, while for
, there are two degenerate vacua. We also obtain the 1-loop quantum
corrections around these vacuum solutions, exactly in the case of and
perturbatively for greater than but close to . Including the
fermions we find that the "chiral" zero modes around the fixed points are
different for . As for the quantum corrections, the
fermionic contributions cancel the singular part of the bosonic contributions
at L=0. Then the total quantum correction has a minimum at the critical length
.Comment: Revtex, 15 pages, 3 eps figure
Kernel functions and B\"acklund transformations for relativistic Calogero-Moser and Toda systems
We obtain kernel functions associated with the quantum relativistic Toda
systems, both for the periodic version and for the nonperiodic version with its
dual. This involves taking limits of previously known results concerning kernel
functions for the elliptic and hyperbolic relativistic Calogero-Moser systems.
We show that the special kernel functions at issue admit a limit that yields
generating functions of B\"acklund transformations for the classical
relativistic Calogero-Moser and Toda systems. We also obtain the
nonrelativistic counterparts of our results, which tie in with previous results
in the literature.Comment: 76 page
Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold
We investigate an operator ordering problem in two-dimensional N=1
supersymmetric model which consists of n real superfields. There arises an
operator ordering problem when the target space is curved. We have to fix the
ordering in quantum operator properly to obtain the correct supersymmetry
algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct
operator ordering. We obtain a supercurrent with correct operator ordering and
a central extension of supersymmetry algebra.Comment: 7 page
Quasi-doubly periodic solutions to a generalized Lame equation
We consider the algebraic form of a generalized Lame equation with five free
parameters. By introducing a generalization of Jacobi's elliptic functions we
transform this equation to a 1-dim time-independent Schroedinger equation with
(quasi-doubly) periodic potential. We show that only for a finite set of
integral values for the five parameters quasi-doubly periodic eigenfunctions
expressible in terms of generalized Jacobi functions exist. For this purpose we
also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics
Classical and quantum three-dimensional integrable systems with axial symmetry
We study the most general form of a three dimensional classical integrable
system with axial symmetry and invariant under the axis reflection. We assume
that the three constants of motion are the Hamiltonian, , with the standard
form of a kinetic part plus a potential dependent on the position only, the
-component of the angular momentum, , and a Hamiltonian-like constant,
, for which the kinetic part is quadratic in the momenta. We find
the explicit form of these potentials compatible with complete integrability.
The classical equations of motion, written in terms of two arbitrary potential
functions, is separated in oblate spheroidal coordinates. The quantization of
such systems leads to a set of two differential equations that can be presented
in the form of spheroidal wave equations.Comment: 17 pages, 3 figure
Semi-classical buckling of stiff polymers
A quantitative theory of the buckling of a worm like chain based on a
semi-classical approximation of the partition function is presented. The
contribution of thermal fluctuations to the force-extension relation that
allows to go beyond the classical Euler buckling is derived in the linear and
non-linear regime as well. It is shown that the thermal fluctuations in the
nonlinear buckling regime increase the end-to-end distance of the semiflexible
rod if it is confined to 2 dimensions as opposed to the 3 dimensional case. Our
approach allows a complete physical understanding of buckling in D=2 and in D=3
below and above the Euler transition.Comment: Revtex, 17 pages, 4 figure
Elasticity of semiflexible polymers in two dimensions
We study theoretically the entropic elasticity of a semi-flexible polymer,
such as DNA, confined to two dimensions. Using the worm-like-chain model we
obtain an exact analytical expression for the partition function of the polymer
pulled at one end with a constant force. The force-extension relation for the
polymer is computed in the long chain limit in terms of Mathieu characteristic
functions. We also present applications to the interaction between a
semi-flexible polymer and a nematic field, and derive the nematic order
parameter and average extension of the polymer in a strong field.Comment: 16 pages, 3 figure
Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation
A hidden nonlinear bosonized supersymmetry was revealed recently in
Poschl-Teller and finite-gap Lame systems. In spite of the intimate
relationship between the two quantum models, the hidden supersymmetry in them
displays essential differences. In particular, the kernel of the supercharges
of the Poschl-Teller system, unlike the case of Lame equation, includes
nonphysical states. By means of Lame equation, we clarify the nature of these
peculiar states, and show that they encode essential information not only on
the original hyperbolic Poschl-Teller system, but also on its singular
hyperbolic and trigonometric modifications, and reflect the intimate relation
of the model to a free particle system.Comment: 10 pages, typos corrected; to appear in J. Phys.
Ince's limits for confluent and double-confluent Heun equations
We find pairs of solutions to a differential equation which is obtained as a
special limit of a generalized spheroidal wave equation (this is also known as
confluent Heun equation). One solution in each pair is given by a series of
hypergeometric functions and converges for any finite value of the independent
variable , while the other is given by a series of modified Bessel functions
and converges for , where denotes a regular singularity.
For short, the preceding limit is called Ince's limit after Ince who have used
the same procedure to get the Mathieu equations from the Whittaker-Hill ones.
We find as well that, when tends to zero, the Ince limit of the
generalized spheroidal wave equation turns out to be the Ince limit of a
double-confluent Heun equation, for which solutions are provided. Finally, we
show that the Schr\"odinger equation for inverse fourth and sixth-power
potentials reduces to peculiar cases of the double-confluent Heun equation and
its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic
Dynamical Casimir effect in oscillating media
We show that oscillations of a homogeneous medium with constant material
coefficients produce pairs of photons. Classical analysis of an oscillating
medium reveals regions of parametric resonance where the electromagnetic waves
are exponentially amplified. The quantum counterpart of parametric resonance is
an exponentially growing number of photons in the same parameter regions. This
process may be viewed as another manifestation of the dynamical Casimir effect.
However, in contrast to the standard dynamical Casimir effect, photon
production here takes place in the entire volume and is not due to time
dependence of the boundary conditions or material constants
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