556 research outputs found
Deformed Schrodinger symmetry on noncommutative space
We construct the deformed generators of Schroedinger symmetry consistent with
noncommutative space. The examples of the free particle and the harmonic
oscillator, both of which admit Schroedinger symmetry, are discussed in detail.
We construct a generalised Galilean algebra where the second central extension
exists in all dimensions. This algebra also follows from the Inonu--Wigner
contraction of a generalised Poincare algebra in noncommuting space.Comment: 9 pages, LaTeX, abstract modified, new section include
SO(2,1) conformal anomaly: Beyond contact interactions
The existence of anomalous symmetry-breaking solutions of the SO(2,1)
commutator algebra is explicitly extended beyond the case of scale-invariant
contact interactions. In particular, the failure of the conservation laws of
the dilation and special conformal charges is displayed for the two-dimensional
inverse square potential. As a consequence, this anomaly appears to be a
generic feature of conformal quantum mechanics and not merely an artifact of
contact interactions. Moreover, a renormalization procedure traces the
emergence of this conformal anomaly to the ultraviolet sector of the theory,
within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio
Efimov effect from functional renormalization
We apply a field-theoretic functional renormalization group technique to the
few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance.
Three systems are considered: one-component bosons with U(1) symmetry,
two-component fermions with U(1)\times SU(2) symmetry and three-component
fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant
unitarity limit for infinite scattering length. The exact solution for the
two-body sector is consistent with the unitary fixed point behavior for all
considered systems. Nevertheless, the numerical three-body solution in the
s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3)
fermions. The Efimov parameter for the one-component bosons and the
three-component fermions is found to be approximately s=1.006, consistent with
the result of Efimov.Comment: 21 pages, 6 figures, minor changes, published versio
Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities
We perform the complete group classification in the class of nonlinear
Schr\"odinger equations of the form
where is an arbitrary
complex-valued potential depending on and is a real non-zero
constant. We construct all the possible inequivalent potentials for which these
equations have non-trivial Lie symmetries using a combination of algebraic and
compatibility methods. The proposed approach can be applied to solving group
classification problems for a number of important classes of differential
equations arising in mathematical physics.Comment: 10 page
Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential
We review some recent results on nonlinear Schrodinger equations with
potential, with emphasis on the case where the potential is a second order
polynomial, for which the interaction between the linear dynamics caused by the
potential, and the nonlinear effects, can be described quite precisely. This
includes semi-classical regimes, as well as finite time blow-up and scattering
issues. We present the tools used for these problems, as well as their
limitations, and outline the arguments of the proofs.Comment: 20 pages; survey of previous result
On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions
We suggest an effective approach to separation of variables in the
Schr\"odinger equation with two space variables. Using it we classify
inequivalent potentials such that the corresponding Schr\" odinger
equations admit separation of variables. Besides that, we carry out separation
of variables in the Schr\" odinger equation with the anisotropic harmonic
oscillator potential and obtain a complete list of
coordinate systems providing its separability. Most of these coordinate systems
depend essentially on the form of the potential and do not provide separation
of variables in the free Schr\" odinger equation ().Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics"
(1995
Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice
We propose the fundamental and two dimensional representation of the Lorentz
groups on a (3+1)-dimensional hypercubic lattice, from which representations of
higher dimensions can be constructed. For the unitary representation of the
discrete translation group we use the kernel of the Fourier transform. From the
Dirac representation of the Lorentz group (including reflections) we derive in
a natural way the wave equation on the lattice for spin 1/2 particles. Finally
the induced representation of the discrete inhomogeneous Lorentz group is
constructed by standard methods and its connection with the continuous case is
discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission
- …