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It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of "What is quantum in quantum randomness", i.e. what is the impact of…
The issue of averaging randomness is addressed, mostly in nuclear physics, but shortly also in QCD. The Feshbach approach, so successful in dealing with the continuum spectrum of the atomic nuclei ("optical model"), is extended to encompass…
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear…
The quantum thermodynamic behavior of small systems is investigated in presence of finite quantum dissipation. We consider the archetype cases of a damped harmonic oscillator and a free quantum Brownian particle. A main finding is that…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…
We employ the quantum jump trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive…
The periodic bounce configurations responsible for quantum tunneling are obtained explicitly and are extended to the finite energy case for minisuperspace models of the Universe. As a common feature of the tunneling models at finite energy…
The effects of quantum and thermal corrections on the dynamics of a damped nonlinearly kicked harmonic oscillator are studied. This is done via the Quantum Langevin Equation formalism working on a truncated moment expansion of the density…
The work is a concept of fundamental importance in thermodynamics. An open question is how to describe the work fluctuation for quantum coherent processes in the presence of initial quantum coherence in the energy basis. With the aim of…
We recall Dirac's early proposals to develop a description of quantum phenomena in terms of a non-commutative algebra in which he suggested a way to construct what he called `quantum trajectories'. Generalising these ideas, we show how they…
We discuss an approach to determine averages of the work, dissipated heat and variation of internal energy of an open quantum system driven by an external classical field. These quantities are measured by coupling the quantum system to a…
Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum…
We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We…
Energy is often partitioned into heat and work by two independent paths corresponding to the change in the eigenenergies or the probability distributions of a quantum system. The discrepancies of the heat and work for various quantum…