Related papers: Path Integrals and Their Application to Dissipativ…
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle…
The quantum many-body problem in condensed phases is often simplified using a quasiparticle description, such as effective mass theory for electron motion in a periodic solid. These approaches are often the basis for understanding many…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free…
The roles of Lie groups in Feynman's path integrals in non-relativistic quantum mechanics are discussed. Dynamical as well as geometrical symmetries are found useful for path integral quantization. Two examples having the symmetry of a…
The phase space $S\times Z$ for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their…
A system of two independent Bosonic Harmonic Oscillators is converted into the respective fourth-order derivative Pais-Uhlenbeck oscillator model. The conversion procedure displays transparently how the quantization of the fourth-order…
The path integral formalism is applied to derive the full partition function of a generalized Su-Schrieffer-Heeger Hamiltonian describing a particle motion in a bath of oscillators. The electronic correlations are computed versus…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a…
In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential $V(x) = \frac{1}{2} \omega^2 x^2 + g x^4$ is presented. Using a path integral formalism, the exact…
Coarse-grained models that preserve hydrodynamics provide a natural approach to study collective properties of soft-matter systems. Here, we demonstrate that commonly used integration schemes in dissipative particle dynamics give rise to…
A continuously measured quantum system may be described by restricted path integrals (RPI) or equivalently by non-Hermitian Hamiltonians. The measured system is then considered as an open system, the influence of the environment being taken…
Master equations describe the quantum dynamics of open systems interacting with an environment. They play an increasingly important role in understanding the emergence of semiclassical behavior and the generation of entropy, both being…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time…