Phase Space Localization and Approach to Thermal Equilibrium for a Class of Open Systems

We analyse the evolution of a quantum oscillator in a finite temperature environment using the quantum state diffusion (QSD) picture. Following a treatment similar to that of reference [7] we identify stationary solutions of the corresponding It\^o equation. We prove their global stability and compute typical time scales characterizing the localization process. The recovery of the density matrix in approximately diagonal form enables us to verify the approach to thermal equilibrium in the long time limit and we comment on the connection between QSD and the decoherent histories approach.Comment: 10 pages, Late

A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity

In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with an asymptotic symmetry and the value of the conserved quantity is defined to be the value of the Hamiltonian which generates the canonical transformation on phase space corresponding to this symmetry. However, such an approach cannot be employed to define `conserved quantities' in a situation where symplectic current can be radiated away (such as occurs at null infinity in general relativity) because there does not, in general, exist a Hamiltonian which generates the given asymptotic symmetry. (This fact is closely related to the fact that the desired `conserved quantities' are not, in general, conserved!) In this paper we give a prescription for defining `conserved quantities' by proposing a modification of the equation that must be satisfied by a Hamiltonian. Our prescription is a very general one, and is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian, although we have not investigated existence and uniqueness issues in the most general contexts. In the case of general relativity with the standard asymptotic conditions at null infinity, our prescription agrees with the one proposed by Dray and Streubel from entirely different considerations.Comment: 39 pages, no figure

On the classical central charge

In the canonical formulation of a classical field theory, symmetry properties are encoded in the Poisson bracket algebra, which may have a central term. Starting from this well understood canonical structure, we derive the related Lagrangian form of the central term.Comment: 23 pages, RevTeX, no figures; introduction improved, a few references adde

Non-Equilibrium Quantum Electrodynamics

We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator for the spinor field is then constructed. We discuss the role of time-dependent renormalization in the propagator and focus on the possibility of obtaining dynamically induced superselection rules. Finally, we derive the master equation for the case of the field being in an one-particle state in a non-relativistic regime and discuss whether EM vacuumm fluctuations are sufficient to produce decoherence in the position basis.Comment: 28 pages, 2 figures. Substantially revised, one important mistake corrected; discussion on decoherence upgraded, section 4 essentially rewritte

The Post-Decoherence Density Matrix Propagator for Quantum Brownian Motion

Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the localization time, (\hbar / \gamma k T )^{\half}, where $\gamma$ is the dissipation and $T$ the temperature of the thermal environment. The localization time is typically greater than the decoherence time, but much shorter than the relaxation time, $\gamma^{-1}$. We use this result to show that the reduced density operator rapidly evolves into a state which is approximately diagonal in a set of generalized coherent states. We thus reproduce, using a completely different method, a result we previously obtained using the quantum state diffusion picture (Phys.Rev. D52, 7294 (1995)). We also go beyond this earlier result, in that we derive an explicit expression for the weighting of each phase space localized state in the approximately diagonal density matrix, as a function of the initial state. For sufficiently long times it is equal to the Wigner function, and we confirm that the Wigner function is positive for times greater than the localization time (multiplied by a number of order 1).Comment: 17 pages, plain Tex, submitted to Physical Review

Quantum State Diffusion, Density Matrix Diagonalization and Decoherent Histories: A Model

We analyse the quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state, using the quantum state diffusion (QSD) picture of Gisin and Percival, in which one associates the usual Markovian master equation for the density operator with a class of stochastic non-linear Schr\"odinger equations. We find stationary solutions to the Ito equation which are Gaussians, localized around a point in phase space undergoing classical Brownian motion. We show that every initial state approaches these stationary solutions in the long time limit. We recover the density operator corresponding to these solutions, and thus show, for this particular model, that the QSD picture effectively supplies a prescription for approximately diagonalizing the density operator in a basis of phase space localized states. The rate of localization is related to the decoherence time, and also to the timescale on which thermal and quantum fluctuations become comparable. We use these results to exemplify the general connection between the QSD picture and the decoherent histories approach.Comment: 32 pages, plain Tex

Definition of “conserved quantities” in general relativity and other theories of gravity within the Hamiltonian framework

Even though, in diffeomorphism covariant theories such as general relativity, there is no notion of the local stress-energy tensor of the gravitational field, so conserved quantities and their fluxes cannot be defined, it is the case that, in general relativity and for asymptotically flat spacetimes, conserved quantities associated with asymptotic symmetries have been defined at spatial and null infinity. With minor exceptions, the definition of “conserved quantities” at null infinity, has little contact with the Hamiltonian formulation of general relativity. We wish to propose a general prescription for defining “conserved quantities” in situations where a Hamiltonian does not exist. We propose a modification on the equation that a Hamiltonian must satisfy via the addition of a “correction term” involving a suitable symplectic potential

Biologic activities of biosynthetic human insulin in healthy volunteers and insulin-dependent diabetic patients monitored by the artificial endocrine pancreas

This study investigates and compares biosynthetic human insulin (BHI) and purified pork insulin, in healthy volunteers and in insulin-dependent diabetic patients, in terms of biologic action, capacity for controlling diabetic patients, and the requirements of the patients on each insulin. The possible importance of this new insulin in the improved long-term control of diabetic patients led to the experimental design of this protocol

Improvement of metabolic control after 3-month use of real-time continuous glucose monitoring in patients with type 1 diabetes: a multicenter study in Greece

Purpose: To assess the efficacy of a real-time continuous glucose monitoring (RT–CGM) system added to insulin pump therapy for 3 months, in sub-optimally controlled adults with type 1 diabetes mellitus (T1D). Methods: This was a prospective, multicenter, non-randomized, post-market release study. A total of 43 adult patients with T1D on insulin pump therapy and inadequate glycemic control (HbA1c > 7.0%) participated in the study. The primary endpoint was the change from baseline HbA1c levels. Secondary objectives were to evaluate the impact of the RT–CGM system on glucose variability, daily insulin requirements, and the frequency of hypoglycemic and ketoacidosis events. Results: At 3 months, the baseline HbA1c values decreased from 8.0 (7.6, 8.7) to 7.1 (6.7, 8.0) % (p < 0.001). Nineteen participants (44.2%) had a posttreatment HbA1c level ≤ 7%. Average total daily insulin requirements, as well as the average number of insulin boluses per day, increased significantly after the use of the RT–CGM system. The number of hypoglycemic events recorded did not differ between the first week and last week of RT–CGM usage, while no severe hypoglycemic episodes, ketoacidosis events, or hospitalizations related to diabetes occurred during the 3-month follow-up period. Conclusion: Addition of a RT–CGM system to insulin pump therapy for 3 months in inadequately controlled patients with T1D resulted in improved HbA1c levels, without increasing the risk of hypoglycemic events. © 2019, Hellenic Endocrine Society