Entropy of Stationary Nonequilibrium Measures of Boundary Driven Symmetric Simple Exclusion Processes

We examine the entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes. In contrast with the Gibbs–Shannon entropy (Bahadoran in J. Stat. Phys. 126(4–5):1069–1082, 2007; Derrida et al. in J. Stat. Phys. 126(4–5):1083–1108, 2007), the entropy of nonequilibrium stationary states differs from the entropy of local equilibrium states.     

The Maxwell Electromagnetic Equations and the Lorentz Type Force Derivation—The Feynman Approach Legacy

R. Feynman’s “heretical” approach (Dyson in Am. J. Phys. 58:209–211, 1990; Dyson in Phys. Today 42(2):32–38, 1989) to deriving the Lorentz force based Maxwell electromagnetic equations is revisited, the its complete legacy is argued both by means of the geometric considerations and its deep relation with the vacuum field theory approach devised (Prykarpatsky et al. in Int. J. Theor. Phys. 49:798–820, 2010; Prykarpatsky et al. in Preprint ICTP, 2008, ). Being completely classical, we reanalyze the Feynman’s derivation from the classical Lagrangian and Hamiltonian points of view and construct its nontrivial relativistic generalization compatible with the vacuum field theory approach.     

On Steady Distributions of Kinetic Models of Conservative Economies

We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat. Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state.     

Triangle Percolation in Mean Field Random Graphs—with PDE

We apply a PDE-based method to deduce the critical time and the size of the giant component of the “triangle percolation” on the Erdős-Rényi random graph process investigated by Derényi, Palla and Vicsek in (Phys. Rev. Lett. 94:160202, [2005]; J. Stat. Phys. 128:219–227, [2007]).     

Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

Kinetic Models with Randomly Perturbed Binary Collisions

We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules which, in some special cases, identify models for granular gases with a background heat bath (Carrillo et al. in Discrete Contin. Dyn. Syst. 24(1):59–81, 2009), and models for wealth redistribution in an agent-based market (Bisi et al. in Commun. Math. Sci. 7:901–916, 2009). Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. The characterization of these stationary states is of independent interest, since we show that they are stationary solutions of different evolution problems, both in the kinetic theory of rarefied gases (Cercignani et al. in J. Stat. Phys. 105:337–352, 2001; Villani in J. Stat. Phys. 124:781–822, 2006) and in the econophysical context (Bisi et al. in Commun. Math. Sci. 7:901–916, 2009).     

A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction

We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. [J. Math. Pures Appl. 82(6):665–683, 2003] to the case of unbounded interaction potentials. We also express the mean-field limit as a “superhamiltonian” system, and state our main result in terms of the Heisenberg-picture dynamics of observables. This is a Egorov-type theorem.     

On Convergence to SLE<Subscript>6</Subscript> I: Conformal Invariance for Certain Models of the Bond-Triangular Type

We show how to extract Cardy’s Formula for a general class of domains given the requisite interior analyticity statement. This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math. Phys. 19:511–565, 2007).     

Reexamining the Security of Controlled Quantum Secure Direct Communication by Using Four Particle Cluster States

A controlled quantum secure direct communication protocol (Zhang et al. in Int. J. Theor. Phys. 48:2971–2976, 2009) by using four particle cluster states was proposed recently. Yang et al. presented an attack with fake entangled particles (FEP attack) and gave an improvement (Yang et al. in Int. J. Theor. Phys. 50:395–400, 2010). In this paper, we reexamine the protocol’s security and discover that, Bob can also take a different attack, disentanglement attack, to obtain Alice’s secret message without controller’s permission. Moreover, our attack strategy also works for Yang’s improvement.     

A Remark on the Decay of Correlations for Mixed-Range Spin Vector Models

In this short note we present some explicit conditions under which the Theorem of Braga et al. (J. Stat. Phys. 129:587–591, 2007) can be extended to spin-spin correlation functions of mixed short-range/long-range ferromagnetic vector spin models in the disordered phase.     

Some Comments on “The Mathematical Universe”

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed “shut-up-and-calculate” approach to physics (Tegmark in Found. Phys. 38:101, 2008; New Sci., September 15th, 2007). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this—at first sight purely philosophical—difference in point of view.     

A Gentle Stochastic Thermostat for Molecular Dynamics

We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys. 128:1321–1336, 2007), and which controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, the new scheme relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that we can recover the canonical distribution. In spite of its stochastic nature, experiments suggest that it introduces a relatively weak perturbative effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is well controlled even in the early stages of a simulation.     

Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes

We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ ^d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry relation with involution map different from time-reversal.     

On ‘light’ fermions and proton stability in ‘big divisor’ D3/D7 large volume compactifications

Building on our earlier work (Misra and Shukla, Nucl. Phys. B 827:112, 2010; Phys. Lett. B 685:347–352, 2010), we show the possibility of generating “light” fermion mass scales of MeV–GeV range (possibly related to the first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-brane restricted to (in principle) stacks of fluxed D7-branes wrapping the “big” divisor Σ _B . This part of the paper is an expanded version of the latter half of Sect. 3 of a published short invited review (Misra, Mod. Phys. Lett. A 26:1, 2011) written by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, and we estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10⁶¹ years. Based on GLSM calculations in (Misra and Shukla, Nucl. Phys. B 827:112, 2010) for obtaining the geometric K?hler potential for the “big divisor,” using further the Donaldson’s algorithm, we also briefly discuss in the first of the two appendices the metric for the Swiss-Cheese Calabi–Yau used, which we obtain and which becomes Ricci flat in the large-volume limit.     

On “Schwinger mechanism for gluon pair production in?the?presence of arbitrary time dependent chromo-electric field”

Recently the paper “Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field” by G.C. Nayak was published [Eur. Phys. J. C 59:715, 2009; ]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the so-called “shift theorem” [] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.     

Improving the Security of Controlled Quantum Secure Direct Communication by Using Four Particle Cluster States Against an Attack with Fake Entangled Particles

A controlled quantum secure direct communication protocol (Zhang et al. Int. J. Theor. Phys. 48:2971–2976, 2009) by using four particle cluster states was proposed recently. The aim of Zhang et al. was that the successful realization of communication between Alice and Bob needed the cooperation of a controller, Charlie. However, we show that the controller Charlie’s role could be excluded unknowingly. Using fake entangled particles and Bell measurement, the dishonest Bob who generates the initial signals can elicit Alice’s secret message without the permission of Charlie. A possible improvement of the protocol is proposed.     

On Consistency of the Quantum-Like Representation Algorithm

In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H ^b|a and H ^a|b . In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA.     

Introducing the fission–fusion reaction process: using a?laser-accelerated Th beam to produce neutron-rich nuclei towards the N=126 waiting point of the r-process

We propose to produce neutron-rich nuclei in the range of the astrophysical r-process (the rapid neutron-capture process) around the waiting point N=126 (Kratz et al. in Prog. Part. Nucl. Phys. 59:147, 2007; Arnould et al. in Phys. Rep. 450:97, 2007; Panov and Janka in Astron. Astrophys. 494:829, 2009) by fissioning a dense laser-accelerated thorium ion bunch in a thorium target (covered by a polyethylene layer, CH₂), where the light fission fragments of the beam fuse with the light fission fragments of the target. Using the ‘hole-boring’ (HB) mode of laser radiation pressure acceleration (RPA) (Robinson et al. in Plasma Phys. Control. Fusion 51:024004, 2009; Henig et al. in Phys. Rev. Lett. 103:245003, 2009; Tajima et al. in Rev. Accel. Sci. Technol. 2:221, 2009) using a high-intensity, short pulse laser, bunches of ²³²Th with solid-state density can be generated very efficiently from a Th layer (ca. 560 nm thick), placed beneath a deuterated polyethylene foil (CD₂ with ca. 520 nm), both forming the production target. Th ions laser-accelerated to about 7 MeV/u will pass through a thin CH₂ layer placed in front of a thicker second Th foil (both forming the reaction target) closely behind the production target and disintegrate into light and heavy fission fragments. In addition, light ions (d,C) from the CD₂ production target will be accelerated as well to about 7 MeV/u, also inducing the fission process of ²³²Th in the second Th layer. The laser-accelerated ion bunches with solid-state density, which are about 10¹⁴ times more dense than classically accelerated ion bunches, allow for a high probability that generated fission products can fuse again when the fragments from the thorium beam strike the Th layer of the reaction target.