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We construct a lattice theory describing a system of interacting nonrelativistic spin s=1/2 fermions at nonzero chemical potential. The theory is applicable whenever the interparticle separation is large compared to the range of the…
The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…
As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or…
We give a review of recent work aimed at understanding the dynamics of gravitational collapse in quantum gravity. Its goal is to provide a non-perturbative computational framework for understanding the emergence of the semi-classical…
Frustrated spin models may lead to the formation of both classical non-collinear spin structures and unique quantum phases including highly entangled quantum spin liquids. Here, we study the entanglement and spatial quantum correlations in…
We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of expanding universes. We discuss recent theoretical results reporting on the production of entanglement in quantum…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
Nuclear systems are treated within a quantum statistical approach. Correlations and cluster formation are relevant for the properties of warm dense matter, but the description is challenging and different approximations are discussed. The…
We investigate the phenomenon of quantum radiation - i.e. the conversion of (virtual) quantum fluctuations into (real) particles induced by dynamical external conditions - for an initial thermal equilibrium state. For a resonantly vibrating…
We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fr\"ohlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons,…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
By resorting to recent results on fermion mixing which show that the Fock space of definite flavor states is unitarily inequivalent to the Fock space of definite mass states, we discuss the phenomenological implications on the neutrino…
We construct a density functional theory for two-dimension electron (hole) gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
The possibility of a novel type of semiconductor quantum dots obtained by spatially modulating the spin-orbit coupling intensity in III-V heterostructures is discussed. Using the effective mass model we predict confined one-electron states…
This article will summarize selected aspects of the semiclassical theory of gravity, which involves a classical gravitational field coupled to quantum matter fields. Among the issues which will be discussed are the role of quantum effects…