# Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion

@article{Matinyan2005AdventuresOT, title={Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion}, author={Sergei G. Matinyan and Berndt Muller}, journal={Journal of Physics A}, year={2005}, volume={39}, pages={45-59} }

We study the quantum mechanical motion in the x2y2 potentials with n = 2, 3, which arise in the spatially homogeneous limit of the Yang–Mills (YM) equations. These systems show strong stochasticity in the classical limit ( = 0) and exhibit a quantum mechanical confinement feature. We calculate the partition function Z(t) going beyond the Thomas–Fermi (TF) approximation by means of the semiclassical expansion using the Wigner–Kirkwood (WK) method. We derive a novel compact form of the…

## 5 Citations

### Adventures of the coupled Yang–Mills oscillators: II. YM–Higgs quantum mechanics

- Physics
- 2006

We continue our study of the quantum mechanical motion in the x2y2 potentials for n = 2, 3, which arise in the spatially homogeneous limit of the Yang–Mills (YM) equations. In the present paper, we…

### LETTER TO THE EDITOR: The partition function in the Wigner Kirkwood expansion

- Physics
- 2006

We study the semiclassical Wigner-Kirkwood (WK) expansion of the partition function $Z(t)$ for arbitrary even homogeneous potentials, starting from the Bloch equation. As is well known, the…

### Entropy production and equilibration in Yang-Mills quantum mechanics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

It is shown that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system, which may be used to track the growth of entropy of a quantum system.

### On the semiclassical limit of the Dirichlet Laplace operator : two-term spectral asymptotics and sharp spectral estimates

- Mathematics
- 2011

In this thesis we study spectral properties of the Dirichlet Laplace operator and related differential and pseudo-differential operators defined on Euclidean domains: the eigenvalues of such…

### Sharp spectral estimates in domains of infinite volume

- Mathematics
- 2010

We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - and therefore on the…

## References

SHOWING 1-10 OF 16 REFERENCES

### Adventures of the coupled Yang–Mills oscillators: II. YM–Higgs quantum mechanics

- Physics
- 2006

We continue our study of the quantum mechanical motion in the x2y2 potentials for n = 2, 3, which arise in the spatially homogeneous limit of the Yang–Mills (YM) equations. In the present paper, we…

### Symmetry decomposition of potentials with channels

- Physics, Mathematics
- 1997

We discuss the symmetry decomposition of the average density of states for the two-dimensional potential and for its three-dimensional generalization . In both problems, the energetically accessible…

### Chaos and Gauge Field Theory

- Physics
- 1995

This text introduces a rapidly growing new research area - the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer…

### On the quantum correction for thermodynamic equilibrium

- Mathematics
- 1932

The probability of a configuration is given in classical theory by the Boltzmann formula exp [— V/hT] where V is the potential energy of this configuration. For high temperatures this of course also…

### Quantum Statistics of Almost Classical Assemblies

- Physics
- 1933

The sum of states of an assembly in statistical equilibrium may be transformed into an integral in phase space, which is analogous to the classical Gibbs phase integral. With the use of an equation…

### Some quantum operators with discrete spectrum but classically continuous spectrum

- Mathematics, Physics
- 1983

### An Introduction to the Theory of Infinite Series

- EconomicsNature
- 1908

THE first impression this book is likely to produce is that, considering its title, it is very big. However, it is not diffuseness that is to blame for this; the fact is that quite a third of the…

### Table of Integrals, Series, and Products

- Mathematics
- 1943

Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special…