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Phase Coherence in Quantum Brownian Motion

Massimo Blasone A, Y. Srivastava, G Vitiello, A. Widom, Infn Salerno, Sezione Di Napoli

Published Jan 1, 1997• 31 citations
OpenAlex

Abstract

The quantum theory of Brownian motion is discussed in the Schwinger version wherein the notion of a coordinate moving forward in time $x(t)$ is replaced by two coordinates, $x_+(t)$ moving forward in time and $x_-(t)$ moving backward in time. The role of the doubling of the degrees of freedom is illustrated for the case of electron beam two slit diffraction experiments. Interference is computed with and without dissipation (described by a thermal bath). The notion of a dissipative interference phase, closely analogous to the Aharonov-Bohm magnetic field induced phase, is explored.

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AIP conference proceedings•Jan 1, 2009•0 citations
The quantum theory of Brownian motion is discussed in the Schwinger version wherein the notion of a coordinate moving forward in time x(t)x(t)x(t) is replaced by two coordinates, x+(t)x_+(t)x+​(t) moving forward in time and x−(t)x_-(t)x−​(t) moving backward in time. The role of the doubling of the degrees of freedom is illustrated for the case of electron beam two slit diffraction experiments. Interference is computed with and without dissipation (described by a thermal bath). The notion of a dissipative interference phase, closely analogous to the Aharonov-Bohm magnetic field induced phase, is explored.
We discuss the various manifestations of quantum decoherence in the forms of dephasing, entanglement with the environment, and revelation of "which-path" information. As a specific example, we consider an electron interference experiment. The coupling of the coherent electrons to the quantized electromagnetic field illustrates all of these versions of decoherence. This decoherence has two equivalent interpretations, in terms of photon emission or in terms of Aharonov-Bohm phase fluctuations. We consider the case when the coherent electrons are coupled to photons in a squeezed vacuum state. The time-averaged result is increased decoherence. However, if only electrons which are emitted during selected periods are counted, the decoherence can be suppressed below the level for the photon vacuum. This is the phenomenon of recoherence. This effect is closely related to the quantum violations of the weak energy condition, and is restricted by similar inequalities. We give some estimates of the magnitude of the recoherence effect and discuss prospects for observing it in an electron interferometry experiment.
The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect. PACS: 02.40.Gh, 11.10.Ef – Key words: noncommutative geometry, gauge theories, dissipation 1
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schrödinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.
Distribution functions defined in accordance with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet spreading and the attenuation of coherence of a pair of wave packets are obtained. The results are exact within the context of linear passive dissipation. It is shown that, contrary to widely accepted current belief, decoherence can occur at high temperature in the absence of dissipation. Expressions for the decoherence time with and without dissipation are obtained that differ from those appearing in earlier discussions.
ABSTRACT\nThe interaction of charged and uncharged particles with intrinsic magnetic moment for the latter with an electromagnetic field in the microworld brings out the actual role of the electromagnetic potentials as emphasized in quantum theory which generate electromagnetic interaction via gauge invariance requirement.\nIn the Aharonov-Bohm (A-B) effect (dealing with two electron coherent beams passing a double slit system), the resulting interference pattern is shifted by the insertion of a very long solenoid between the two electron beams with an influence described by the magnetic vector\npotential A on the electron wave functions. Aharonov and Casher presented the complement of the Aharonov-Bohm effect involving the role of the electric scalar potential co on a beam of neutrons each carrying an internal magnetic dipole moment. A similar shift in the interference pattern is found involving two coherent neutron beam interference, where the solenoid in the A-B arrangement is replaced by an electric line charge, and the electrons by polarized neutrons. The effective Hamiltonian describing the two effects is used to determine the interference pattern.\nThe experiment to verify the existence of the Aharonov-Bohm effect which have been performed using an electron holography with a small toroidal ferromagnetic substance confining a magnetic flux by Tonomura in 1982 is discussed. The Aharonov-Casher effect, which was conducted using a Bonse-Hart single-crystal neutron interferometer by A. Cirnmino in 1989, is also discussed. Both experimental results lead to the same phenomenon: a phase shift in the observed pattern interference quantitatively explained as caused by the influence of the proper component of the electrodynamic potentials.\n\nKey Word: Kuantum, Aharonov- cahser
Given that it is now possible to observe the interference of molecules with comparatively numerous internal degrees of freedom, we might wonder what role these extra degrees of freedom play in the traditional double‐slit experiment. Here we seek to understand the effect of these degrees of freedom in an Aharonov‐Bohm type experiment. We find, perhaps unsurprisingly that an ionised object can exhibit the Aharonov‐Bohm effect in a manner which is independent of its internal structure. Meanwhile, the Aharonov‐Bohm type effects involving objects with magnetic, or electric dipole moments (the Aharonov‐Casher and He‐McKellar‐Wilkens effects, respectively) depend explicitly upon the structure. When—due to some specified dynamics of the internal variables—an object’s dipole moment changes during the experiment, we find that the corresponding phase shift depends upon the time average and variance of the internal dynamics. Furthermore, given that the internal dynamics are, to an extent, dependent upon the centre of mass motion there is also a small, transient loss of coherence associated with each internal degree of freedom.