Representation of nonequilibrium steady states in large mechanical systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.Comment: 27 pages, 3 figure

Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagwa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which "heat" is replaced by the "excess heat", is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komtatsu et al.Comment: 19 pages, 2 figure

A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify that this generalized FDT coincides with known results for n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.Comment: 34 pages, Revte

Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation

The kangaroo process (KP) is characterized by various forms of the covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.Comment: 22 pages (RevTeX) and 4 figure

Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7

It is known that large class of classical string solutions in the type IIB AdS_5xS^5 background is related to the Neumann and Neumann-Rosochatius integrable systems, including spiky strings and giant magnons. It is also interesting if these integrable systems can be associated with some membrane configurations in M-theory. We show here that this is indeed the case by presenting explicitly several types of membrane embedding in AdS_4xS^7 with the searched properties.Comment: LaTeX, 17 pages, no figures;v2: comments and citations added;v3: 20 pages, new subsection, explanations, comments and references added; v4: some typos fixed, to appear in JHE

Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory

The quantum time evolution of \phi^4-field theory for a spatially homogeneous system in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym equations including the tadpole and sunset self-energies. Whereas the tadpole self-energy yields a dynamical mass, the sunset self-energy is responsible for dissipation and an equilibration of the system. In particular we address the dynamics of the spectral (`off-shell') distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. The investigation explicitly demonstrates that the only translation invariant solutions representing the stationary fixed points of the coupled equation of motions are those of full thermal equilibrium. They agree with those extracted from the time integration of the Kadanoff-Baym equations in the long time limit. Furthermore, a detailed comparison of the full quantum dynamics to more approximate and simple schemes like that of a standard kinetic (on-shell) Boltzmann equation is performed. Our analysis shows that the consistent inclusion of the dynamical spectral function has a significant impact on relaxation phenomena. The different time scales, that are involved in the dynamical quantum evolution towards a complete thermalized state, are discussed in detail. We find that far off-shell 1 3 processes are responsible for chemical equilibration, which is missed in the Boltzmann limit. Finally, we address briefly the case of (bare) massless fields. For sufficiently large couplings $\lambda$ we observe the onset of Bose condensation, where our scheme within symmetric \phi^4-theory breaks down.Comment: 77 pages, 26 figure

Detection of the blazar S4 0954+65 at very-high-energy with the MAGIC telescopes during an exceptionally high optical state

The very high energy (VHE ¿ 100 GeV) -ray MAGIC observations of the blazar S4 0954+65, were triggered by an exceptionally high flux state of emission in the optical. This blazar has a disputed redshift of z = 0.368 or z ¿ 0.45 and an uncertain classification among blazar subclasses. The exceptional source state described here makes for an excellent opportunity to understand physical processes in the jet of S4 0954+65 and thus contribute to its classification. Methods. We investigated the multiwavelength (MWL) light curve and spectral energy distribution (SED) of the S4 0954+65 blazar during an enhanced state in February 2015 and have put it in context with possible emission scenarios. We collected photometric data in radio, optical, X-ray, and ¿-ray. We studied both the optical polarization and the inner parsec-scale jet behavior with 43 GHz data. Results. Observations with the MAGIC telescopes led to the first detection of S4 0954+65 at VHE. Simultaneous data with Fermi-LAT at high energy ¿-ray(HE, 100 MeV < E < 100 GeV) also show a period of increased activity. Imaging at 43 GHz reveals the emergence of a new feature in the radio jet in coincidence with the VHE flare. Simultaneous monitoring of the optical polarization angle reveals a rotation of approximately 100. Conclusions. The high emission state during the flare allows us to compile the simultaneous broadband SED and to characterize it in the scope of blazar jet emission models. The broadband spectrum can be modeled with an emission mechanism commonly invoked for flat spectrum radio quasars (FSRQs), that is, inverse Compton scattering on an external soft photon field from the dust torus, also known as external Compton. The light curve and SED phenomenology is consistent with an interpretation of a blob propagating through a helical structured magnetic field and eventually crossing a standing shock in the jet, a scenario typically applied to FSRQs and low-frequency peaked BL Lac objects (LBL). © ESO 2018.The financial support of the German BMBF and MPG, the Italian INFN and INAF, the Swiss National Fund SNF, the ERDF under the Spanish MINECO (FPA2015-69818-P, FPA2012-36668, FPA2015-68378-P, FPA2015-69210-C6-2-R, FPA2015-69210-C6-4-R, FPA2015-69210-C6-6-R, AYA2015-71042-P, AYA2016-76012-C3-1-P, ESP2015-71662-C2-2-P, CSD2009-00064), and the Japanese JSPS and MEXT is gratefully acknowledged. This work was also supported by the Spanish Centro de Excelencia “Severo Ochoa” SEV-2012-0234 and SEV-2015-0548, and Unidad de Excelencia “María de Maeztu” MDM-2014-0369, by the Croatian Science Foundation (HrZZ) Project IP-2016-06-9782 and the University of Rijeka Project 13.12.1.3.02, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, the Polish National Research Centre grant UMO-2016/22/M/ST9/00382 and by the Brazilian MCTIC, CNPq, and FAPERJ. IA acknowledges support by a Ramón y Cajal grant of the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain. The research at the IAA–CSIC was supported in part by the MINECO through grants AYA2016–80889–P, AYA2013–40825–P, and AYA2010–14844, and by the regional government of Andalucía through grant P09–FQM–4784.Peer Reviewe