66 research outputs found
Quantum Inverse Square Interaction
Hamiltonians with inverse square interaction potential occur in the study of
a variety of physical systems and exhibit a rich mathematical structure. In
this talk we briefly mention some of the applications of such Hamiltonians and
then analyze the case of the N-body rational Calogero model as an example. This
model has recently been shown to admit novel solutions, whose properties are
discussed.Comment: Talk presented at the conference "Space-time and Fundamental
Interactions: Quantum Aspects" in honour of Prof. A.P.Balachandran's 65th
birthday, Vietri sul Mare, Italy, 26 - 31 May, 2003, Latex file, 9 pages.
Some references added in the replaced versio
Semi-classical scattering in two dimensions
The semi-classical limit of quantum-mechanical scattering in two dimensions
(2D) is developed. We derive the Wentzel-Kramers-Brillouin and Eikonal results
for 2D scattering. No backward or forward glory scattering is present in 2D.
Other phenomena, such as rainbow or orbiting do show up.Comment: 6 page
Hidden Degeneracy in the Brick Wall Model of Black Holes
Quantum field theory in the near-horizon region of a black hole predicts the
existence of an infinite number of degenerate modes. Such a degeneracy is
regulated in the brick wall model by the introduction of a short distance
cutoff. In this Letter we show that states of the brick wall model with non
zero energy admit a further degeneracy for any given finite value of the
cutoff. The black hole entropy is calculated within the brick wall model taking
this degeneracy into account. Modes with complex frequencies however do not
exhibit such a degeneracy.Comment: 8 pages, Latex fil
Quantization of exciton in magnetic field background
The possible mismatch between the theoretical and experimental absorption of
the edge peaks in semiconductors in a magnetic field background may arise due
to the approximation scheme used to analytically calculate the absorption
coefficient. As a possible remedy we suggest to consider nontrivial boundary
conditions on x-y plane by in-equivalently quantizing the exciton in background
magnetic field. This inequivalent quantization is based on von Neumann's method
of self-adjoint extension, which is characterized by a parameter \Sigma. We
obtain bound state solution and scattering state solution, which in general
depend upon the self-adjoint extension parameter \Sigma. The parameter \Sigma
can be used to fine tune the optical absorption coefficient K(\Sigma) to match
with the experiment.Comment: 5 pages, 1 figur
Non-commutativity as a measure of inequivalent quantization
We show that the strength of non-commutativity could play a role in
determining the boundary condition of a physical problem. As a toy model we
consider the inverse square problem in non-commutative space. The scale
invariance of the system is known to be explicitly broken by the scale of
non-commutativity \Theta. The resulting problem in non-commutative space is
analyzed. It is shown that despite the presence of higher singular potential
coming from the leading term of the expansion of the potential to first order
in \Theta, it can have a self-adjoint extensions. The boundary conditions are
obtained, belong to a 1-parameter family and related to the strength of
non-commutativity.Comment: 4 pages, 2 figures, revte
On the joint distribution of the maximum and its position of the Airy2 process minus a parabola
The maximal point of the Airy2 process minus a parabola is believed to
describe the scaling limit of the end-point of the directed polymer in a random
medium, which was proved to be true for a few specific cases. Recently two
different formulas for the joint distribution of the location and the height of
this maximal point were obtained, one by Moreno Flores, Quastel and Remenik,
and the other by Schehr. The first formula is given in terms of the Airy
function and an associated operator, and the second formula is expressed in
terms of the Lax pair equations of the Painleve II equation. We give a direct
proof that these two formulas are the same.Comment: 15 pages, no figure, minor revision, to appear in J.Math.Phy
Self-Adjointness of Generalized MIC-Kepler System
We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian,
obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We
have shown that for \tilde l=0, the system admits a 1-parameter family of
self-adjoint extensions and for \tilde l \neq 0 but \tilde l <{1/2}, it has
also a 1-parameter family of self-adjoint extensions.Comment: 11 pages, Latex, no figur
Dipole binding in a cosmic string background due to quantum anomalies
We propose quantum dynamics for the dipole moving in cosmic string background
and show that the classical scale symmetry of a particle moving in cosmic
string background is still restored even in the presence of dipole moment of
the particle. However, we show that the classical scale symmetry is broken due
to inequivalent quantization of the the non-relativistic system. The
consequence of this quantum anomaly is the formation of bound state in the
interval \xi\in(-1,1). The inequivalent quantization is characterized by a
1-parameter family of self-adjoint extension parameter \Sigma. We show that
within the interval \xi\in(-1,1), cosmic string with zero radius can bind the
dipole and the dipole does not fall into the singularity.Comment: Accepted for publication in Phys. Rev.
Return interval distribution of extreme events and long term memory
The distribution of recurrence times or return intervals between extreme
events is important to characterize and understand the behavior of physical
systems and phenomena in many disciplines. It is well known that many physical
processes in nature and society display long range correlations. Hence, in the
last few years, considerable research effort has been directed towards studying
the distribution of return intervals for long range correlated time series.
Based on numerical simulations, it was shown that the return interval
distributions are of stretched exponential type. In this paper, we obtain an
analytical expression for the distribution of return intervals in long range
correlated time series which holds good when the average return intervals are
large. We show that the distribution is actually a product of power law and a
stretched exponential form. We also discuss the regimes of validity and perform
detailed studies on how the return interval distribution depends on the
threshold used to define extreme events.Comment: 8 pages, 6 figure
Relativistic Quantum Scattering on a Cone
We study the relativistic quantum mechanical scattering of a bosonic particle
by an infinite straight cosmic string, considering the non-minimal coupling
between the bosonic field and the scalar curvature. In this case, an effective
two-dimensional delta-function interaction takes place besides the usual
topological scattering and a renormalization procedure is necessary in order to
treat the problem that appears in connection with the delta-function.Comment: 22 pages, LATEX fil
- …