79 citations · 1.2k across the 123 of their papers we have counts for
21 papers · 1 filter
Quantized Noncommutative Riemann Manifolds and Stochastic Processes: The theoretical foundations of the square root of Brownian motion
Marco Frasca, Alfonso Farina, Moawia Alghalith
We lay the theoretical and mathematical foundations of the square root of Browniam motion and we prove the existence of such a process. In doing so, we consider Brownian motion on…
Noncommutative geometry and stochastic processes
Marco Frasca
The recent analysis on noncommutative geometry, showing quantization of the volume for the Riemannian manifold entering the geometry, can support a view of quantum mechanics as ari…
Consistency of the adiabatic theorem and perturbation theory
Marco Frasca
We present an analysis of the adiabatic approximation to understand when it applies, in view of the recent criticisms and studies for the validity of the adiabatic theorem. We poin…
Thermodynamic Limit and Decoherence: Rigorous Results
Marco Frasca
Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution…
A Quantum Many-Body Instability in the Thermodynamic Limit
Marco Frasca
Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends…
Stern-Gerlach Experiment and Bohm Limit
Marco Frasca
Stern-Gerlach experiment is a paradigm of measurement theory in quantum mechanics. Notwithstanding several analysis given in literature, no clear understanding of the apparent coll…
1/N-expansion for the Dicke model and the decoherence program
Marco Frasca
An analysis of the Dicke model, N two-level atoms interacting with a single radiation mode, is done using the Holstein-Primakoff transformation. The main aim of the paper is to sho…
Dynamical decoherence in a cavity with a large number of two-level atoms
Marco Frasca
We consider a large number of two-level atoms interacting with the mode of a cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the Holstein-Primakoff trans…
Strong Coupling Perturbation Theory in Quantum Mechanics
Marco Frasca
We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, th…
General Theorems on Decoherence in the Thermodynamic Limit
Marco Frasca
We extend the results on decoherence in the thermodynamic limit [M. Frasca, Phys. Lett. A {\bf 283}, 271 (2001)] to general Hamiltonians. It is shown that N independent particles,…
Does decoherence in the thermodynamic limit exist?
Marco Frasca
Paper withdrawn due to an error into the equations of the probability amplitudes.
Dynamical disappearance of superposition states in the thermodynamic limit
Marco Frasca
It is shown that a macroscopic superposition state of radiation, strongly interacting with an ensemble of two-level atoms, is removed generating a coherent state describing a class…
A modern review of the two-level approximation
Marco Frasca
The paradigm of the two-level atom is revisited and its perturbative analysis is discussed in view of the principle of duality in perturbation theory. The models we consider are a…
Ultraviolet analysis of one dimensional quantum systems
Marco Frasca
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to mo…
Classical states and decoherence by unitary evolution in the thermodynamic limit
Marco Frasca
It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics.…
Rabi oscillations and macroscopic quantum superposition states
Marco Frasca
A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong coupling regime. It is shown that, in agreement with…
Non-relativistic quantum electrodynamics for strong laser-atom interaction
Marco Frasca
A formulation of quantum electrodynamics is given that applies to atoms in a strong laser field by perturbation theory in a non-relativistic regime. Dipole approximation is assumed…
Perturbative study of multiphoton processes in the tunneling regime
Marco Frasca
A perturbative study of the Schrödinger equation in a strong electromagnetic field with dipole approximation is accomplished in the Kramers-Henneberger frame. A prove that just odd…
Theory of dressed states in quantum optics
Marco Frasca
The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In…
The Higher Orders of the Theory of Strong Perturbations in Quantum Mechanics and the Secularity Problem
Marco Frasca
We solve the higher order equations of the theory of the strong perturbations in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by assuming that, at the leading…
The Leading Order of the Theory of Strong Perturbations in Quantum Mechanics
Marco Frasca
We prove that, for a quantum system that undergoes a strong perturbation, the solution of the leading order equation of the strong field approximation (M.Frasca, Phys. Rev. A, {\bf…