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This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second…
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…
A new approach to cosmological perturbation theory has been recently introduced by Bartelmann et al., relying on nonequilibrium statistical theory of classical particles, and treating the gravitational interaction perturbatively. They…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
A recent suggestion has been made that the hydrogen bound state spectrum should not depend on the number of spatial dimensions. It is pointed out here that the uncertainty principle implies that such differences must exist and that a…
A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
Control of multi-level quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
We assume that particles are point-like objects even when not observed. We report on the consequences of our assumption within the realm of quantum theory. An important consequence is the necessity of vacuum fields to account for particle…
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
We consider a two-dimensional interacting Fermi system which displays a nematic phase within mean-field theory. The system is analyzed using a non-perturbative renormalization-group scheme. We find that order-parameter fluctuations can…
Quantum gates (unitary gates) on physical systems are usually implemented by controlling the Hamiltonian dynamics. When full descriptions of the Hamiltonians parameters is available, the set of implementable quantum gates is easily…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an…