Quantum Operation Time Reversal

The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes towards equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.Comment: 4 page

On the Quantum Jarzynski Identity

In this note, we will discuss how to compactly express and prove the Jarzynski identity for an open quantum system with dissipative dynamics. We will avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the system, and instead measure the heat flow from the environment. We represent the measurement of heat flow with Hermitian map superoperators that act on the system density matrix. Hermitian maps provide a convenient and compact representation of sequential measurement and correlation functions.Comment: 4 page

Microscopic reversibility of quantum open systems

The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to externally perturbed large quantum open systems. The time-dependent external perturbation acts on the subsystem during a transient duration, and subsequently the perturbation is switched off so that the total system would thermalize. We concern with the transition probability for the subsystem between the initial and final eigenstates of the subsystem. In the course of time evolution, the energy is irreversibly exchanged between the subsystem and reservoir. The time reversed probability is given by the reversal of the protocol and the initial ensemble. Microscopic reversibility equates the time forward and reversed probabilities, and therefore appears as a thermodynamic symmetry for open quantum systems.Comment: numerical demonstration is correcte

Transient fluctuation theorem in closed quantum systems

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure

Angular and Energy Distribution of Cross Sections for Electron Production by 50-300-keV-Proton Impacts on N\u3csub\u3e2\u3c/sub\u3e, O\u3csub\u3e2\u3c/sub\u3e, Ne, and Ar

Cross sections differential in angle and ejection energy for electron production by proton impact on nitrogen, oxygen, neon, and argon have been measured using electrostatic analysis and counting of individual electrons. The range of proton energies was 50-300 keV, the angles ranged from 10° to 160°, and the electron energies were measured from 1.5 to 1057 eV. Integrations over angle and/or electron energy yielded singly differential and total electron production cross sections. Our total cross sections for oxygen fall halfway between previous data of deHeer et al. and Hooper et al., but our argon cross sections agree better with deHeer et al. Cross sections for electron ejection in the backward hemisphere are much greater for these multishell targets than for hydrogen and helium. The momentum-energy conservation hump which was prominent in hydrogen is less conspicuous for these gases

Angular and Energy Distribution of Cross Sections for Electron Production by 50-300-keV-Proton Impacts on N\u3csub\u3e2\u3c/sub\u3e, O\u3csub\u3e2\u3c/sub\u3e, Ne, and Ar

Cross sections differential in angle and ejection energy for electron production by proton impact on nitrogen, oxygen, neon, and argon have been measured using electrostatic analysis and counting of individual electrons. The range of proton energies was 50-300 keV, the angles ranged from 10° to 160°, and the electron energies were measured from 1.5 to 1057 eV. Integrations over angle and/or electron energy yielded singly differential and total electron production cross sections. Our total cross sections for oxygen fall halfway between previous data of deHeer et al. and Hooper et al., but our argon cross sections agree better with deHeer et al. Cross sections for electron ejection in the backward hemisphere are much greater for these multishell targets than for hydrogen and helium. The momentum-energy conservation hump which was prominent in hydrogen is less conspicuous for these gases

A feasibility, randomised controlled trial of a complex breathlessness intervention in idiopathic pulmonary fibrosis (BREEZE-IPF): study protocol

Introduction Idiopathic pulmonary fibrosis (IPF) is a chronic and progressive lung disease that causes breathlessness and cough that worsen over time, limiting daily activities and negatively impacting quality of life. Although treatments are now available that slow the rate of lung function decline, trials of these treatments have failed to show improvement in symptoms or quality of life. There is an immediate unmet need for evidenced-based interventions that improve patients' symptom burden and make a difference to everyday living. This study aims to assess the feasibility of conducting a definitive randomised controlled trial of a holistic, complex breathlessness intervention in people with IPF. Methods and analysis The trial is a two-centre, randomised controlled feasibility trial of a complex breathlessness intervention compared with usual care in patients with IPF. 50 participants will be recruited from secondary care IPF clinics and randomised 1:1 to either start the intervention within 1 week of randomisation (fast-track group) or to receive usual care for 8 weeks before receiving the intervention (wait-list group). Participants will remain in the study for a total of 16 weeks. Outcome measures will be feasibility outcomes, including recruitment, retention, acceptability and fidelity of the intervention. Clinical outcomes will be measured to inform outcome selection and sample size calculation for a definitive trial. Ethics and dissemination Yorkshire and The Humber – Bradford Leeds Research Ethics Committee approved the study protocol (REC 18/YH/0147). Results of the main trial and all secondary end-points will be submitted for publication in a peer-reviewed journal

The length of time's arrow

An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence between trajectory probability distributions of an experiment and its time-reversed conjugate. Among other interesting properties, the length of time's arrow bounds the average dissipation and determines the difficulty of accurately estimating free energy differences in nonequilibrium experiments