A characterization of intrinsic reciprocity

This paper studies a game-theoretic model in which players have preferences over their strategies. These preferences vary with the strategic context. The paper further assumes that each player has an ordering over an opponent's strategies that describes the niceness of these strategies. It introduces a condition that insures that the weight on an opponent's utility increases if and only if the opponent chooses a nicer strategy. © 2007 Springer Verlag.Segal thanks SSHRCC and Sobel thanks the Guggenheim Foundation, NSF, and the Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Ciencia (Spain) for financial support.Peer Reviewe

Preferences and social influence

Interaction between decision makers may affect their preferences. We consider a setup in which each individual is characterized by two sets of preferences: his unchanged core preferences and his behavioral preferences. Each individual has a social influence function that determines his behavioral preferences given his core preferences and the behavioral preferences of other individuals in his group. Decisions are made according to behavioral preferences. The paper considers different properties of these social influence functions and their effect on equilibrium behavior. We illustrate the applicability of our model by considering decision making by a committee that has a deliberation stage prior to votin

Wigner function and Schroedinger equation in phase space representation

We discuss a family of quasi-distributions (s-ordered Wigner functions of Agarwal and Wolf) and its connection to the so called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space they have completely different interpretation.Comment: 6 page

Quantum fluctuation theorem for heat exchange in the strong coupling regime

We study quantum heat exchange in a multi-state impurity coupled to two thermal reservoirs. Allowing for strong system-bath interactions, we show that a steady-state heat exchange fluctuation theorem holds, though the dynamical processes nonlinearly involve the two reservoirs. We accomplish a closed expression for the cumulant generating function, and use it obtain the heat current and its cumulants in a nonlinear thermal junction, the two-bath spin-boson model

Non-Equilibrium Quantum Dissipation

Dissipative processes in non-equilibrium many-body systems are fundamentally different than their equilibrium counterparts. Such processes are of great importance for the understanding of relaxation in single molecule devices. As a detailed case study, we investigate here a generic spin-fermion model, where a two-level system couples to two metallic leads with different chemical potentials. We present results for the spin relaxation rate in the nonadiabatic limit for an arbitrary coupling to the leads, using both analytical and exact numerical methods. The non-equilibrium dynamics is reflected by an exponential relaxation at long times and via complex phase shifts, leading in some cases to an "anti-orthogonality" effect. In the limit of strong system-lead coupling at zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with {\it voltage difference} activation. This is analogous to the equilibrium spin-boson model, where at strong coupling and high temperatures the spin excitation rate manifests temperature activated Gaussian behavior. We find that there is no simple linear relationship between the role of the temperature in the bosonic system and a voltage drop in a non-equilibrium electronic case. The two models also differ by the orthogonality-catastrophe factor existing in a fermionic system, which modifies the resulting lineshapes. Implications for current characteristics are discussed. We demonstrate the violation of pair-wise Coulomb gas behavior for strong coupling to the leads. The results presented in this paper form the basis of an exact, non-perturbative description of steady-state quantum dissipative systems

Exact dynamics of interacting qubits in a thermal environment: Results beyond the weak coupling limit

We demonstrate an exact mapping of a class of models of two interacting qubits in thermal reservoirs to two separate spin-bath problems. Based on this mapping, exact numerical simulations of the qubits dynamics can be performed, beyond the weak system-bath coupling limit. Given the time evolution of the system, we study, in a numerically exact way, the dynamics of entanglement between pair of qubits immersed in boson thermal baths, showing a rich phenomenology, including an intermediate oscillatory behavior, the entanglement sudden birth, sudden death, and revival. We find that stationary entanglement develops between the qubits due to their coupling to a thermal environment, unlike the isolated qubits case in which the entanglement oscillates. We also show that the occurrence of entanglement sudden death in this model depends on the portion of the zero and double excitation states in the subsystem initial state. In the long-time limit, analytic expressions are presented at weak system-bath coupling, for a range of relevant qubit parameters

Loop Groups and Discrete KdV Equations

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al. arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are also given, the lowest order discretization of the first nontrivial equation in the hierarchy, and a "second order" discretization of b_t=b_x. The former, which is given the name "full lattice KdV" has the (potential) KdV equation as a standard continuum limit. For each discretization a Backlund transformation is given and soliton content analyzed. The full lattice KdV system has, like KdV itself, solitons of all speeds, whereas both other discretizations studied have a limited range of speeds, being discretizations of an equation with solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur

On the Thermal Symmetry of the Markovian Master Equation

The quantum Markovian master equation of the reduced dynamics of a harmonic oscillator coupled to a thermal reservoir is shown to possess thermal symmetry. This symmetry is revealed by a Bogoliubov transformation that can be represented by a hyperbolic rotation acting on the Liouville space of the reduced dynamics. The Liouville space is obtained as an extension of the Hilbert space through the introduction of tilde variables used in the thermofield dynamics formalism. The angle of rotation depends on the temperature of the reservoir, as well as the value of Planck's constant. This symmetry relates the thermal states of the system at any two temperatures. This includes absolute zero, at which purely quantum effects are revealed. The Caldeira-Leggett equation and the classical Fokker-Planck equation also possess thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov transformation in related fields and discuss the effects of the symmetry on the shape of a Gaussian wave packet.Comment: Eqs.(64a), (65a)-(68) are correcte

Translational outcomes in a full gene deletion of ubiquitin protein ligase E3A rat model of Angelman syndrome.

Angelman syndrome (AS) is a rare neurodevelopmental disorder characterized by developmental delay, impaired communication, motor deficits and ataxia, intellectual disabilities, microcephaly, and seizures. The genetic cause of AS is the loss of expression of UBE3A (ubiquitin protein ligase E6-AP) in the brain, typically due to a deletion of the maternal 15q11-q13 region. Previous studies have been performed using a mouse model with a deletion of a single exon of Ube3a. Since three splice variants of Ube3a exist, this has led to a lack of consistent reports and the theory that perhaps not all mouse studies were assessing the effects of an absence of all functional UBE3A. Herein, we report the generation and functional characterization of a novel model of Angelman syndrome by deleting the entire Ube3a gene in the rat. We validated that this resulted in the first comprehensive gene deletion rodent model. Ultrasonic vocalizations from newborn Ube3am-/p+ were reduced in the maternal inherited deletion group with no observable change in the Ube3am+/p- paternal transmission cohort. We also discovered Ube3am-/p+ exhibited delayed reflex development, motor deficits in rearing and fine motor skills, aberrant social communication, and impaired touchscreen learning and memory in young adults. These behavioral deficits were large in effect size and easily apparent in the larger rodent species. Low social communication was detected using a playback task that is unique to rats. Structural imaging illustrated decreased brain volume in Ube3am-/p+ and a variety of intriguing neuroanatomical phenotypes while Ube3am+/p- did not exhibit altered neuroanatomy. Our report identifies, for the first time, unique AS relevant functional phenotypes and anatomical markers as preclinical outcomes to test various strategies for gene and molecular therapies in AS

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivariant de Rham cohomology in terms of derived functors developed earlier for the special case where the Lie groupoid is an ordinary Lie group, viewed as a Lie groupoid with a single object; in that theory over a Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a posteriori object. We prove that, given a locally trivial Lie groupoid G and a smooth G-manifold f over the space B of objects of G, the resulting G-equivariant de Rham theory of f boils down to the ordinary equivariant de Rham theory of a vertex manifold relative to the corresponding vertex group, for any vertex in the space B of objects of G; this implies that the equivariant de Rham cohomology introduced here coincides with the stack de Rham cohomology of the associated transformation groupoid whence this stack de Rham cohomology can be characterized as a relative derived functor. We introduce a notion of cone on a Lie-Rinehart algebra and in particular that of cone on a Lie algebroid. This cone is an indispensable tool for the description of the requisite monads.Comment: 47 page