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In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control…
A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
Tunneling of a particle through a potential barrier remains one of the most remarkable quantum phenomena. Owing to advances in laser technology, electric fields comparable to those electrons experience in atoms are readily generated and…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the…
We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…
Quantum systems under electric fields provide a powerful framework for uncovering and controlling novel quantum phases, especially in low-dimensional systems with strong correlations. In this work, we investigate quantum phase transitions…
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of…
The phase diagram of the two-dimensional ANNNI model has long been theoretically debated. Extremely long structural correlations and relaxation times further result in numerical simulations making contradictory predictions. Here, we…
Transport through nanosystems is treated within the second order von Neumann approach. This approach bridges the gap between rate equations which neglect level broadening and cotunneling, and the transmission formalism, which is essentially…
Using the formal analysis made by Bohm in his book, {\em "Quantum theory"}, Dover Publications Inc. New York (1979), to calculate approximately the phase time for a transmitted and the reflected wave packets through a potential barrier, we…
Neutrino scillations cannot arise from an initial isolated one particle state if four-momentum is conserved. The transition matrix element is generally squared and summed over all final states with no interference between orthogonal final…
Tunnelling is one of the most paradigmatic and evocative phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from SQUID magnetometers to superconducting qubits for quantum…