Unified Treatment of Quantum Fluctuation Theorem and Jarzynski Equality in Terms of microscopic reversibility

There are two related theorems which hold even in far from equilibrium, namely fluctuation theorem and Jarzynski equality. Fluctuation theorem states the existence of symmetry of fluctuation of entropy production, while Jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes. On the other hand, relationship between these theorems was investigated by Crooks for the classical stochastic systems. In this letter, we derive quantum analogues of fluctuation theorem and Jarzynski equality microscopic reversibility condition. In other words, the quantum analogue of the work by Crooks is presented.Comment: 7pages, revised versio

RASCAL: calculation of graph similarity using maximum common edge subgraphs

A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection

Legal Issues Pertaining to Community Based Fisheries Management

National and intergovernmental regulation of fisheries has not prevented many failures of fisheries management around the world. New approaches to improving the environmental sustainability of fisheries have included the certification of fisheries harvested by sustainable means, and the ecolabelling of fish and seafood products from certified fisheries. The intention is to use the power of markets as an incentive to induce more sustainable fisheries. To date, only a relatively small number of fisheries have been certified, and these have been predominantly in developed countries. Critiques from developing countries of ecolabelling, as currently formulated, focus on five general areas: a) legitimacy and credibility; b) a mismatch between certification requirements and the reality of tropical small-scale fisheries; c) potential distortions to existing practices and livelihoods; d) equity and feasibility; and e) perceived barriers to trade.This paper reviews these developing country concerns on the basis of already certified fisheries, and on experiences from forestry, aquaculture and the aquarium industry, and also examines precedents and trends in international environmental and trade issues. It suggests that ecolabelling as currently practiced is unlikely to be widely adopted in Asian countries. Certification may have sporadic success in some eco-conscious, or niche, markets but it is unlikely to stimulate global improvement of fisheries management.The paper argues that to avoid the controversy that accompanies ecolabelling, the focus should be on revision of national fisheries management and not on an ad hoc approach to individual fisheries. Improvements in fisheries management, the equitable treatment of fishing sub-sectors and stakeholders within management schemes, and the prospect of reaping increased value-added from fisheries all require government acceptance of needs and actions. Governments should be encouraged to enter into broad coalitions to improve aspects of fisheries management, and to enhance efforts to develop locally relevant indicator systems for fisheries and for the ecosystem approach. Governments of developing countries must also first address the difficult questions of access to and tenure arrangements for their fisheries, as these are essential prerequisites for successful certification and product labeling. They will also need to legislate on the form and conduct of the postharvest chain and product control, as, in export markets, these are outside the control ofthe fishing communities. International agreement and clarity on trade, environmental (and health) standards affecting fisheries will augment national efforts. Advocacy coalitions that include governments, rather than extraterritorial imposition of labelling schemes, are required

Stochastic mean-field dynamics for fermions in the weak coupling limit

Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond mean-field is first presented. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states $D=| \Phi_a > < \Phi_b |/$ where $| \Phi_a >$ and $| \Phi_b >$ are antisymmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical $^{40}$Ca nucleus under the influence of a statistical ensemble of two-body contact interaction. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. Restricting to two particles-two holes residual interaction, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as $D = | \Phi >$ is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave-functions is given.Comment: Enlarged version, 10 pages, 2 figure

Bogoliubov dynamics of condensate collisions using the positive-P representation

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description as the number of realisations grows. The numerical effort grows linearly with the size of the computational lattice. We benchmark the efficiency and accuracy of our description against Wigner distribution and exact positive-P methods. We consider its regime of applicability, and show that it is the most efficient method in the common situation - when the total particle number in the system is insufficient for a truncated Wigner treatment.Comment: 9 pages. 5 figure

Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids

A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations allows one to obtain the full quantum dynamics for much longer times than is possible using an exact treatment directly. A collision of sodium BECs with 1.x10^5 atoms is simulated, in a regime that is difficult to describe semiclassically. The uncertainty of physical quantities depends on the statistics of the full quantum prediction. Cutoffs are minimised to a discretization of the Hamiltonian. The technique presented is quite general and extension to other systems is considered.Comment: Published version. Broader background and discussion, slightly shortened, less figures in epaps. Research part unchanged. Article + epaps (4+4 pages), 8 figure

The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow

We study an experimentally realizable system containing stable black hole-white hole acoustic horizons in toroidally trapped Bose-Einstein condensates - the quantum de Laval nozzle. We numerically obtain stationary flow configurations and assess their stability using Bogoliubov theory, finding both in hydrodynamic and non-hydrodynamic regimes there exist dynamically unstable regions associated with the creation of positive and negative energy quasiparticle pairs in analogy with the gravitational Hawking effect. The dynamical instability takes the form of a two mode squeezing interaction between resonant pairs of Bogoliubov modes. We study the evolution of dynamically unstable flows using the truncated Wigner method, which confirms the two mode squeezed state picture of the analogue Hawking effect for low winding number.Comment: 12 pages, 10 figure

Parametric Oscillation with Squeezed Vacuum Reservoirs

Employing the quantum Hamiltonian describing the interaction of two-mode light (signal-idler modes) generated by a nondegenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master equation. The corresponding Fokker-Planck equation for the Q-function is then solved employing a propagator method developed in Ref. \cite{1}. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal-idler modes are in squeezed states and the squeezing occurs in the first quadrature. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in the first quadrature can be achieved.Comment: 16 page