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Georg Junker

Publications and source records attributed to Georg Junker.

33 records · Page 2Linked to original sources
arXiv1998

Quantum and classical stochastic dynamics: Exactly solvable models by supersymmetric methods

A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of drift-potentials on the real line as well as on the half line is constructed for which the associated Fokker-Planck equation can be solved exactly. Explicit drift potentials, which describe mono-, bi-, meta-or unstable systems, are constructed and their decay rates and modes are given in closed form.

quant-ph↗
arXiv1998

Coherent-state path-integral approach for constrained fermion systems

The coherent-state path-integral representation for the propagator of fermionic systems subjected to first-class constraints is constructed. As in the bosonic case the importance of path-integral measures for Lagrange multipliers is emphasized. One example is discussed in some detail.

hep-th↗
arXiv1998

Conditionally exactly solvable potentials: A supersymmetric construction method

We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of one-dimensional potentials are constructed whose corresponding Schrödinger eigenvalue problem can be solved exactly under certain conditions of the potential parameters. Examples of quantum systems on the real line, the half line as well as on some finite interval are studied in detail.

quant-ph↗
arXiv1997

Supersymmetric Construction of Exactly Solvable Potentials and Non-Linear Algebras

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators together with the Hamilton operator form a non-linear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator, respectively.

quant-ph↗
arXiv1997

Coherent-state quantization of constrained fermion systems

The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral measures for Lagrange multipliers, which in this case are in general expected to be elements of a Grassmann algebra, is emphasized. Several examples with first- and second-class constraints are discussed.

quant-ph↗
arXiv1996

Path-Integral Aspects of Supersymmetric Quantum Mechanics

In this talk we briefly review the concept of supersymmetric quantum mechanics using a model introduced by Witten. A quasi-classical path-integral evaluation for this model is performed, leading to a so-called supersymmetric quasi-classical quantization condition. Properties of this quantization condition are compared with those derived from the standard WKB approach.

hep-th↗
arXiv1995

Classical and quasi-classical aspects of supersymmetric quantum mechanics

A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the classical equations of motion are given and their properties are discussed in some detail. The corresponding quantum model is constructed by canonical quantization. The quantum model is analyzed by Feynman's path integral within a stationary-phase approximation. A quasi-classical quantization rule is derived, which is applicable when supersymmetry is exact or spontaneously broken.

hep-th↗
arXiv1995

Classical and quantum dynamics of the n-dimensional kicked rotator

The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar to that of the one-dimensional model. For the quantum dynamics such a result is not expected as in this case the evolution does depend in a very complicated way on the number n of degrees of freedom. In the limit n --> infinity we find the free undistrubed quantum motion. For finite values of n (1<=n<=26) we study numerically the quantum dynamics. Here, we always find localization independent of the actual number of degrees of freedom.

chao-dyn↗
arXiv1994

Supersymmetric classical mechanics

We study the classical properties of a supersymmetric system which is often used as a model for supersymmetric quantum mechanics. It is found that the classical dynamics of the bosonic as well as the fermionic degrees of freedom is fully described by a so--called quasi--classical solution. We also comment on the importance of this quasi--classical solution in the semi--classical treatment of the supersymmetric quantum model.

cond-mat↗
arXiv1994

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.

cond-mat↗
arXiv1994

Recent Developments in Supersymmetric Quantum Mechanics

Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of Pauli's Hamiltonian are also considered. In particular, the paramagnetisation of a non-interacting electron gas is related to a modified version of Witten's index. We also show that the supersymmetry in this system provides a new counter example for the paramagnetic conjecture.

cond-mat↗