Related papers: Levy Flights over Quantum Paths
"Particle"-trajectories are defined as integrable $dx_\mu dp^\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the…
Due to the advent of Quantum Mechanics' 100th anniversary in 2025, we wrote this review paper in order to present a discussion that addresses the foundations of this theory. And since the creation of this Mechanics and other quantum…
Geometric correlations between jets as part of hard processes or in addition to hard processes are key ingredients to many LHC analyses. Fox--Wolfram moments systematically describe these correlations in terms of spherical harmonics. These…
Multiple scattering of light by resonant vapor is characterized by L\'evy-type superdiffusion with a single-step size distribution $p(x)\propto 1/x^{1+\alpha}$. We investigate L\'evy flight of light in a hot rubidium vapor…
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
We introduce a new class of Fokker-Planck equations associated with an effective generalized thermodynamical framework. These equations describe a gas of Langevin particles in interaction. The free energy can take various forms which can…
Trajectories of a Bohmian particle confined in time-dependent cylindrical and spherical traps are computed for both contracting and expanding boxes. Quantum effective force is considered in arbitrary directions. It is seen that in contrast…
Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for…
We here put forward a new path-integral over Hilbert space and show that it reproduces quantum mechanics exactly. This approach works by optimizing the generating functional under a variation of the final state; it is hence an example of a…
The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a Brownian system subjected to a Levy stable random force. The corresponding classical transport equations for the Wigner function are…
The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general…
We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigen-energy…
Using the linear local induction approximation, we investigated the self-induced motion of a vortex line that corresponds to the motion of a particle in quantum mechanics. Concerning Kelvin waves, the effective Schr\"odinger equation,…
In this paper, we consider a large class of purely discontinuous rotationally symmetric Levy processes. We establish sharp two-sided estimates for the transition densities of such processes killed upon leaving an open set D. When D is a…
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…
A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed and demonstrated using full configuration interaction (FCI) simulations and…
The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point…
Plane partitions naturally appear in many problems of statistical physics and quantum field theory, for instance, in the theory of faceted crystals and of topological strings on Calabi-Yau threefolds. In this paper a connection is made…
We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…