Steady state fluctuations of the dissipated heat for a quantum stochastic model

We introduce a quantum stochastic dynamics for heat conduction. A multi-level subsystem is coupled to reservoirs at different temperatures. Energy quanta are detected in the reservoirs allowing the study of steady state fluctuations of the entropy dissipation. Our main result states a symmetry in its large deviation rate function.Comment: 41 pages, minor changes, published versio

'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion

Recently, several authors studied small quantum systems weakly coupled to free boson or fermion fields at positive temperature. All the approaches we are aware of employ complex deformations of Liouvillians or Mourre theory (the infinitesimal version of the former). We present an approach based on polymer expansions of statistical mechanics. Despite the fact that our approach is elementary, our results are slightly sharper than those contained in the literature up to now. We show that, whenever the small quantum system is known to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad equation) in the weak coupling limit, and the Markov approximation is exponentially mixing, then the weakly coupled system approaches a unique invariant state that is perturbatively close to its Markov approximation.Comment: 23 pages, v2-->v3: Revised version: The explanatory section 1.7 has changed and Section 3.2 has been made more explici

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics

We extend the mathematical theory of quantum hypothesis testing to the general $W^*$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.Comment: 60 page

A new numerical approach to Anderson (de)localization

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with small disorder allows states that are dynamically delocalized with positive probability. This approach is based on a recent result by Abakumov-Liaw-Poltoratski which is rooted in the study of spectral behavior under rank-one perturbations, and states that every non-zero vector is almost surely cyclic for the singular part of the operator. The numerical work presented is rather simplistic compared to other numerical approaches in the field. Further, this method eliminates effects due to boundary conditions. While we carried out the numerical experiment almost exclusively in the case of the two dimensional discrete random Schroedinger operator, we include the setup for the general class of Anderson models called Anderson-type Hamiltonians. We track the location of the energy when a wave packet initially located at the origin is evolved according to the discrete random Schroedinger operator. This method does not provide new insight on the energy regimes for which diffusion occurs.Comment: 15 pages, 8 figure

The Spectral Structure of the Electronic Black Box Hamiltonian

We give results on the absence of singular continuous spectrum of the one-particle Hamiltonian underlying the electronic black box model.Comment: 11 page

Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases

We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We establish that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature $T$, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics--they need not be in a state of thermal equilibrium. The temperature $T$ to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy $k_{\mathrm B}T$ is equal to an appropriately defined average of the scatterers' kinetic energy. In the equilibrated state, particle motion is diffusive

A note on the Landauer principle in quantum statistical mechanics

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared

Influence of CAN fertilizer and seed inoculation with NS Nitragin on glycine max plant on pseudogley soil type

Soybean [Glycine max (L.) Merr.] is the most important legume because it is an essential source of dietary protein and oil for animal feed and food production. Good soil with wellplanned program of fertilization is the main factor of soybean production. Soybean yield will be reduced when essential nutrients are deficient. Sufficient soil fertility combined with a well-planned fertilization program is a main component for high soybean production. The aim of this investigation was to estimate the effects of fertilization and seed inoculation on height of soybean plant in humid year. Two factors were tested: 1. CAN fertilization and 2. seed inoculation. Four treatments of CAN fertilization were tested: Control - 0 kg N ha-1; 50 kg N ha-1; 100 kg N ha-1 and 150 kg N ha-1. Two factors of seed inoculation (SI) were tested: Without SI and with SI. Results showed that fertilizers and seed inoculation significantly increased the values of soybean productivity. Cost effective is the application of 50 kg N ha-1 and it is recommended on the basis of this study

The Diffusion of the Magnetization Profile in the XX-model

By the $C^*$-algebraic method, we investigate the magnetization profile in the intermediate time of diffusion. We observe a transition from monotone profile to non-monotone profile. This transition is purely thermal.Comment: Accepted for publication in Phys. Rev.

One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results

17 pagesInternational audienceThe spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new formulae take place in a representation which links, in a suitable way, the energies $-\infty$ and $+\infty$, and which emphasizes the role of $\pm m$. Finally, a topological version of Levinson's theorem is deduced, with the threshold effects at $\pm m$ automatically taken into account