We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic po... more We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.
ABSTRACT We consider families of random non-unitary contraction operators defined as deformations... more ABSTRACT We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure results about the location and nature of the spectrum of such non-normal operators as a function of their parameters. We relate these results to the analysis of certain random quantum walks, the dynamics of which can be studied by means of iterates of such random non-unitary contraction operators.
Abstract. We present a rigorous analysis of the Bardeen-Cooper-Schrieer (BCS) model for general p... more Abstract. We present a rigorous analysis of the Bardeen-Cooper-Schrieer (BCS) model for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the non- linear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain eectiv e linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not van- ish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.
We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic po... more We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.
ABSTRACT We consider families of random non-unitary contraction operators defined as deformations... more ABSTRACT We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure results about the location and nature of the spectrum of such non-normal operators as a function of their parameters. We relate these results to the analysis of certain random quantum walks, the dynamics of which can be studied by means of iterates of such random non-unitary contraction operators.
Abstract. We present a rigorous analysis of the Bardeen-Cooper-Schrieer (BCS) model for general p... more Abstract. We present a rigorous analysis of the Bardeen-Cooper-Schrieer (BCS) model for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the non- linear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain eectiv e linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not van- ish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.
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Papers by Eman Hamza