Related papers: Quantum-mechanical tunneling: differential operato…
We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…
Picard--Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its…
We study the quantum mechanical motion of massive particles in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock and allows particle velocities to be determined.…
Traditionally quantum tunneling in a static SQUID is studied on the basis of a classical trajectory in imaginary time under a two-dimensional potential barrier. The trajectory connects a potential well and an outer region crossing their…
A quantum kinetic formalism is developed to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The approach provides the means to follow…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the…
We study the corrections to adiabatic dynamics of two coupled quantum dot spin-qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an…
A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QW admit, as their continuum limit, a well-known equation of Physics. In arXiv:1803.01015 the QW is…
The Wheeler-DeWitt equation is investigated and used to examine a state after a quantum tunneling with gravity. To make arguments definite we treat a discretized version of the Wheeler-DeWitt equation and adopt the WKB method. We expand an…
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
We present a classical and quantum analysis of a particle confined in a three-dimensional paraboloidal cavity formed by two confocal paraboloids. Classically, the system is integrable and presents three independent constants of motion,…
We investigate the quantum dynamics of a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential shape with a superconducting circuit comprised of a loop interrupted…
Methods for computing the regularized determinants of fluctuation operators are being developed. The results follow from the fact that these determinants can be expressed by eigenmodes of the fluctuation operator. As an application the…
Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the…