Ultracoherence and Canonical Transformations

The (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.Comment: 24 page

Applications of Canonical Transformations

Canonical transformations are defined and discussed along with the exponential, the coherent and the ultracoherent vectors. It is shown that the single-mode and the $n$-mode squeezing operators are elements of the group of canonical transformations. An application of canonical transformations is made, in the context of open quantum systems, by studying the effect of squeezing of the bath on the decoherence properties of the system. Two cases are analyzed. In the first case the bath consists of a massless bosonic field with the bath reference states being the squeezed vacuum states and squeezed thermal states while in the second case a system consisting of a harmonic oscillator interacting with a bath of harmonic oscillators is analyzed with the bath being initially in a squeezed thermal state.Comment: 14 page

A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page

Initial correlations effects on decoherence at zero temperature

We consider a free charged particle interacting with an electromagnetic bath at zero temperature. The dipole approximation is used to treat the bath wavelengths larger than the width of the particle wave packet. The effect of these wavelengths is described then by a linear Hamiltonian whose form is analogous to phenomenological Hamiltonians previously adopted to describe the free particle-bath interaction. We study how the time dependence of decoherence evolution is related with initial particle-bath correlations. We show that decoherence is related to the time dependent dressing of the particle. Moreover because decoherence induced by the T=0 bath is very rapid, we make some considerations on the conditions under which interference may be experimentally observed.Comment: 16 pages, 1 figur

Phase Diffusion in Quantum Dissipative Systems

We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum nondemoliton type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decoherence as well as dissipation. The system is taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a harmonic oscillator, and the environment is modeled as a bath of harmonic oscillators, starting out in a squeezed thermal state. The impact of the different environmental parameters on the dynamics of the quantum phase distribution for the system starting out in various initial states, is explicitly brought out. An interesting feature that emerges from our work is that the relationship between squeezing and temperature effects depends on the type of system-bath interaction. In the case of quantum nondemolition type of interaction, squeezing and temperature work in tandem, producing a diffusive effect on the phase distribution. In contrast, in case of a dissipative interaction, the influence of temperature can be counteracted by squeezing, which manifests as a resistence to randomization of phase. We make use of the phase distributions to bring out a notion of complementarity in atomic systems. We also study the dispersion of the phase using the phase distributions conditioned on particular initial states of the system.Comment: Accepted for publication in Physical Review A; changes in section V; 20 pages, 12 figure

Euclidean Supergravity in Terms of Dirac Eigenvalues

It has been recently shown that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possiblity that the eigenvalues of the Dirac operator might play the same role in the case of supergravity. It is shown that for this purpose some primary constraints on covariant phase space as well as secondary constraints on the eigenspinors must be imposed. The validity of primary constraints under covariant transport is further analyzed. It is show that in the this case restrictions on the tanget bundle and on the spinor bundle of spacetime arise. The form of these restrictions is determined under some simplifying assumptions. It is also shown that manifolds with flat curvature of tangent bundle and spinor bundle and spinor bundle satisfy these restrictons and thus they support the Dirac eigenvalues as global observables.Comment: Misprints and formulae corrected; to appear in Phys. Rev.

The Gisin-Percival stochastic Schrödinger equation from standard quantum filtering theory

We show that the quantum state diffusion equation of Gisin and Percival, driven by complex Wiener noise, is equivalent up to a global stochastic phase to quantum trajectory models. With an appropriate feedback scheme, we set up an analogue continuous measurement model with exactly simulates the Gisin-Percival quantum state diffusion.Comment: Originally submitted to a Theoretical Physics journal but rejected with the re-submission instructions to drop my discussion and references to the papers of Gisin and Percival, which I consider unethical. To be now submitted to an appropriate Mathematical Physics journal instea

Dystonia in neurodegeneration with brain iron accumulation: outcome of bilateral pallidal stimulation

Neurodegeneration with brain iron accumulation encompasses a heterogeneous group of rare neurodegenerative disorders that are characterized by iron accumulation in the brain. Severe generalized dystonia is frequently a prominent symptom and can be very disabling, causing gait impairment, difficulty with speech and swallowing, pain and respiratory distress. Several case reports and one case series have been published concerning therapeutic outcome of pallidal deep brain stimulation in dystonia caused by neurodegeneration with brain iron degeneration, reporting mostly favourable outcomes. However, with case studies, there may be a reporting bias towards favourable outcome. Thus, we undertook this multi-centre retrospective study to gather worldwide experiences with bilateral pallidal deep brain stimulation in patients with neurodegeneration with brain iron accumulation. A total of 16 centres contributed 23 patients with confirmed neurodegeneration with brain iron accumulation and bilateral pallidal deep brain stimulation. Patient details including gender, age at onset, age at operation, genetic status, magnetic resonance imaging status, history and clinical findings were requested. Data on severity of dystonia (Burke Fahn Marsden Dystonia Rating Scale—Motor Scale, Barry Albright Dystonia Scale), disability (Burke Fahn Marsden Dystonia Rating Scale—Disability Scale), quality of life (subjective global rating from 1 to 10 obtained retrospectively from patient and caregiver) as well as data on supportive therapy, concurrent pharmacotherapy, stimulation settings, adverse events and side effects were collected. Data were collected once preoperatively and at 2–6 and 9–15 months postoperatively. The primary outcome measure was change in severity of dystonia. The mean improvement in severity of dystonia was 28.5% at 2–6 months and 25.7% at 9–15 months. At 9–15 months postoperatively, 66.7% of patients showed an improvement of 20% or more in severity of dystonia, and 31.3% showed an improvement of 20% or more in disability. Global quality of life ratings showed a median improvement of 83.3% at 9–15 months. Severity of dystonia preoperatively and disease duration predicted improvement in severity of dystonia at 2–6 months; this failed to reach significance at 9–15 months. The study confirms that dystonia in neurodegeneration with brain iron accumulation improves with bilateral pallidal deep brain stimulation, although this improvement is not as great as the benefit reported in patients with primary generalized dystonias or some other secondary dystonias. The patients with more severe dystonia seem to benefit more. A well-controlled, multi-centre prospective study is necessary to enable evidence-based therapeutic decisions and better predict therapeutic outcomes

Real-Time CARS Imaging Reveals a Calpain-Dependent Pathway for Paranodal Myelin Retraction during High-Frequency Stimulation

High-frequency electrical stimulation is becoming a promising therapy for neurological disorders, however the response of the central nervous system to stimulation remains poorly understood. The current work investigates the response of myelin to electrical stimulation by laser-scanning coherent anti-Stokes Raman scattering (CARS) imaging of myelin in live spinal tissues in real time. Paranodal myelin retraction at the nodes of Ranvier was observed during 200 Hz electrical stimulation. Retraction was seen to begin minutes after the onset of stimulation and continue for up to 10 min after stimulation was ceased, but was found to reverse after a 2 h recovery period. The myelin retraction resulted in exposure of Kv 1.2 potassium channels visualized by immunofluorescence. Accordingly, treating the stimulated tissue with a potassium channel blocker, 4-aminopyridine, led to the appearance of a shoulder peak in the compound action potential curve. Label-free CARS imaging of myelin coupled with multiphoton fluorescence imaging of immuno-labeled proteins at the nodes of Ranvier revealed that high-frequency stimulation induced paranodal myelin retraction via pathologic calcium influx into axons, calpain activation, and cytoskeleton degradation through spectrin break-down