Related papers: Random Unitary Models and their Localization Prope…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
Many-body quantum dynamics defined on a spatial lattice and in discrete time -- either as stroboscopic Floquet systems or quantum circuits -- has been an active area of research for several years. Being discrete in space and time, a natural…
The dynamics of a one dimensional quantum walker on the lattice with two internal degrees of freedom, the coin states, is considered. The discrete time unitary dynamics is determined by the repeated action of a coin operator in U(2) on the…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
The quantum dynamics of atoms subjected to pairs of closely-spaced $\delta$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We find the unitary…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We investigate the properties of electronic states in two and three-dimensional quasiperiodic structures: the generalized Rauzy tilings. Exact diagonalizations, limited to clusters with a few thousands sites, suggest that eigenstates are…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…