Michael Gallis - Academia.edu (original) (raw)
Papers by Michael Gallis
Physical Review A, Jan 1, 1990
Physical Review A, Jan 1, 1991
Eprint Arxiv Quant Ph 0210054, Oct 8, 2002
The majority of quantum open system models in the literature are simplistic in the sense that the... more The majority of quantum open system models in the literature are simplistic in the sense that they only explicitly account for that part of the environment that directly interacts with the system of interest. A quantum open system with an open environment is examined using the projection operator method in the weak coupling limit. The openness of environment is modelled by nonunitary evolution of the Lindblad form. Under certain conditions, the resulting master equation for the system is insensitive to the initial state of the environment and to initial entanglements between the system and environment for time scales greater than the environment relaxation timescales. For the particular case of an environment consisting of a harmonic oscillator bath, the resulting master equations are demonstrated to have the algebraic form for completely positive evolution. The open environment model is illustrated for the particular case of a system linearly coupled to an oscillator bath.
Phys Rev a, 1992
Several quantum open-system models have been examined recently that dynamically reduce the off-di... more Several quantum open-system models have been examined recently that dynamically reduce the off-diagonal terms of the density operator in the position representation by incorporating the effects of interaction with external degrees of freedom. A recent model [M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990)] includes explicit dependence on the spatial correlations of the decoherence rate of the off-diagonal elements (in the position representation) of the density operator. In this paper, we use influence-functional techniques to examine the effect of an external potential that randomly varies as function of position and time, which leads to a natural characterization of the decay rate of the coherence between spatially separated states in terms of the spatial correlations of the potential, and the corresponding fluctuating forces. We obtain the effective master equations for short environment relaxation time scales, and discuss the similarities and differences between the effects of random external potentials versus the effects of interactions with external degrees of freedom, such as that recently investigated by Stern, Aharonov, and Imry [Phys. Rev. A 41, 3436 (1990)].
Phys Rev a, 1996
Zurek, Habib, and Paz [Phys. Rev. Lett. 70, 1187 (1993)] have characterized the set of states of ... more Zurek, Habib, and Paz [Phys. Rev. Lett. 70, 1187 (1993)] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment and shown that coherent states are maximal for the particular environment model examined. To generalize these results, I consider entropy production within the Lindblad theory of open systems, treating environment effects perturbatively. I characterize the maximally predicitive states that emerge from several forms of effective dynamics, including decoherence from spatially correlated noise. Under a variety of conditions, coherent states emerge as the maximal states.
Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for m... more Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for
Decoherence and dissipation in quantum systems has been studied extensively in the context of Qua... more Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.
The Physics Teacher, 2002
Physical Review A, 1996
1187] have characterized the set of states of maximal stability defined as the set of states havi... more 1187] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment, and shown that coherent states are maximal for the par-
Physical Review A, 1992
Several quantum open-system models have been examined recently that dynamically reduce the off-di... more Several quantum open-system models have been examined recently that dynamically reduce the off-diagonal terms of the density operator in the position representation by incorporating the effects of interaction with external degrees of freedom. A recent model [M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990)] includes explicit dependence on the spatial correlations of the decoherence rate of the off-diagonal elements (in the position representation) of the density operator. In this paper, we use influence-functional techniques to examine the effect of an external potential that randomly varies as function of position and time, which leads to a natural characterization of the decay rate of the coherence between spatially separated states in terms of the spatial correlations of the potential, and the corresponding fluctuating forces. We obtain the effective master equations for short environment relaxation time scales, and discuss the similarities and differences between the effects of random external potentials versus the effects of interactions with external degrees of freedom, such as that recently investigated by Stern, Aharonov, and Imry [Phys. Rev. A 41, 3436 (1990)].
Physical Review A, 1993
We propose a family of master equations for local quantum dissipation. The master equations are c... more We propose a family of master equations for local quantum dissipation. The master equations are constructed in the form of Lindblad generators, with the constraints that the dissipation be strictly linear (i.e. ohmic), isotropic and translationally invariant. The resulting master equations are given in both the Schrödinger and Heisenberg forms. We obtain fluctuation-dissipation relations, and discuss the relaxation of average kinetic energy to effective thermal equilibrium values. We compare our results for one dimension to the Dekker master equation [H. Dekker, Phys. Rep. 80, 1 (1981)], which can be interpreted as a low length scale approximation of our model, as well as the Caldeira-Leggett master equation [A. O. Caldeira and A. J. Leggett, Physica (Utrecht) 121 A, 587 (1983)]. PACS number 3.65.-w, 3.65.Bz, 5.40.+j Typeset Using REVTEX
Physical Review A, Jan 1, 1990
Physical Review A, Jan 1, 1991
Eprint Arxiv Quant Ph 0210054, Oct 8, 2002
The majority of quantum open system models in the literature are simplistic in the sense that the... more The majority of quantum open system models in the literature are simplistic in the sense that they only explicitly account for that part of the environment that directly interacts with the system of interest. A quantum open system with an open environment is examined using the projection operator method in the weak coupling limit. The openness of environment is modelled by nonunitary evolution of the Lindblad form. Under certain conditions, the resulting master equation for the system is insensitive to the initial state of the environment and to initial entanglements between the system and environment for time scales greater than the environment relaxation timescales. For the particular case of an environment consisting of a harmonic oscillator bath, the resulting master equations are demonstrated to have the algebraic form for completely positive evolution. The open environment model is illustrated for the particular case of a system linearly coupled to an oscillator bath.
Phys Rev a, 1992
Several quantum open-system models have been examined recently that dynamically reduce the off-di... more Several quantum open-system models have been examined recently that dynamically reduce the off-diagonal terms of the density operator in the position representation by incorporating the effects of interaction with external degrees of freedom. A recent model [M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990)] includes explicit dependence on the spatial correlations of the decoherence rate of the off-diagonal elements (in the position representation) of the density operator. In this paper, we use influence-functional techniques to examine the effect of an external potential that randomly varies as function of position and time, which leads to a natural characterization of the decay rate of the coherence between spatially separated states in terms of the spatial correlations of the potential, and the corresponding fluctuating forces. We obtain the effective master equations for short environment relaxation time scales, and discuss the similarities and differences between the effects of random external potentials versus the effects of interactions with external degrees of freedom, such as that recently investigated by Stern, Aharonov, and Imry [Phys. Rev. A 41, 3436 (1990)].
Phys Rev a, 1996
Zurek, Habib, and Paz [Phys. Rev. Lett. 70, 1187 (1993)] have characterized the set of states of ... more Zurek, Habib, and Paz [Phys. Rev. Lett. 70, 1187 (1993)] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment and shown that coherent states are maximal for the particular environment model examined. To generalize these results, I consider entropy production within the Lindblad theory of open systems, treating environment effects perturbatively. I characterize the maximally predicitive states that emerge from several forms of effective dynamics, including decoherence from spatially correlated noise. Under a variety of conditions, coherent states emerge as the maximal states.
Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for m... more Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for
Decoherence and dissipation in quantum systems has been studied extensively in the context of Qua... more Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.
The Physics Teacher, 2002
Physical Review A, 1996
1187] have characterized the set of states of maximal stability defined as the set of states havi... more 1187] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment, and shown that coherent states are maximal for the par-
Physical Review A, 1992
Several quantum open-system models have been examined recently that dynamically reduce the off-di... more Several quantum open-system models have been examined recently that dynamically reduce the off-diagonal terms of the density operator in the position representation by incorporating the effects of interaction with external degrees of freedom. A recent model [M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990)] includes explicit dependence on the spatial correlations of the decoherence rate of the off-diagonal elements (in the position representation) of the density operator. In this paper, we use influence-functional techniques to examine the effect of an external potential that randomly varies as function of position and time, which leads to a natural characterization of the decay rate of the coherence between spatially separated states in terms of the spatial correlations of the potential, and the corresponding fluctuating forces. We obtain the effective master equations for short environment relaxation time scales, and discuss the similarities and differences between the effects of random external potentials versus the effects of interactions with external degrees of freedom, such as that recently investigated by Stern, Aharonov, and Imry [Phys. Rev. A 41, 3436 (1990)].
Physical Review A, 1993
We propose a family of master equations for local quantum dissipation. The master equations are c... more We propose a family of master equations for local quantum dissipation. The master equations are constructed in the form of Lindblad generators, with the constraints that the dissipation be strictly linear (i.e. ohmic), isotropic and translationally invariant. The resulting master equations are given in both the Schrödinger and Heisenberg forms. We obtain fluctuation-dissipation relations, and discuss the relaxation of average kinetic energy to effective thermal equilibrium values. We compare our results for one dimension to the Dekker master equation [H. Dekker, Phys. Rep. 80, 1 (1981)], which can be interpreted as a low length scale approximation of our model, as well as the Caldeira-Leggett master equation [A. O. Caldeira and A. J. Leggett, Physica (Utrecht) 121 A, 587 (1983)]. PACS number 3.65.-w, 3.65.Bz, 5.40.+j Typeset Using REVTEX