1,721,016 research outputs found
Quantum Mechanics and Stochastic Mechanics for Compatible Observables at Different Times
Full text linkBohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the
presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of
compatible position observables on stationary states agree with quantum mechanics only in the case
of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory,
in particular no stochastic process, can reproduce the quantum mechanical correlations of position
variables of noninteracting systems at different times
Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
No full textWe study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding degrees of freedom are traced out, the effective Hamiltonian of the particles converges in resolvent sense to a self-adjoint Schrödinger operator with an additional potential, depending on the state of the field. Moreover, we explicitly derive the expression of such a potential for a large class of field states and show that, for certain special sequences of states, the effective potential is trapping. In addition, we prove convergence of the ground-state energy of the full system to a suitable effective variational problem involving the classical state of the field
Magnetic perturbations of anyonic and Aharonov-Bohm Schrödinger operators
No full textWe study the Hamiltonian describing two anyons moving in a plane in the presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schrödinger operator. We also discuss the associated model describing a quantum particle immersed in a magnetic field with a local Aharonov–Bohm singularity. For a special class of magnetic potentials, we provide a complete classification of all possible self-adjoint extensions
Hamiltonians for two-anyon systems
Full text linkWe study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for noninteracting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schrödinger operator. We finally extend the results in presence of a two-body radial interaction
A Two-Particle Quantum System with Zero-Range Interaction
Full text linkWe study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schr\"{o}dinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators
Quasi-classical dynamics of quantum particles interacting with radiation
Full text linkWe study the effective dynamics of microscopic models of quantum particles interacting with a bosonic radiation in the quasi-classical limit. In the regime considered, the field has high intensity and can be described as a macroscopic object and suitably approximated by its classical counterpart, while the particles retain their quantum nature. We prove that the field evolves freely, playing the role of a classical environment, while the particles dynamics is generated by an effective Schroedinger operator and averaged over the possible configurations of the field
A Quantum Model of Feshbach Resonances
Full text linkWe consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel coupling, and in the non-perturbative one. We provide an expansion of the effective scattering length near the resonances, via a detailed study of an effective Lippmann–Schwinger equation with energy-dependent potential
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