JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter iResearch App Facebook

Search Issue | RSS Feeds RSS
Next Issue

Jan 2010

Volume 51, Issue 1, Articles (01xxxx)

Issue Cover Spotlight Figure
back to top
RSS Feeds
FREE

Introduction to Special Issue: Journal of Mathematical Physics turns 50

Bruno L. Z. Nachtergaele

J. Math. Phys. 51, 015101 (2010); http://dx.doi.org/10.1063/1.3293460 (3 pages)

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Abstract Unavailable
Show PACS
01.30.Ww Editorials

Space and time from translation symmetry

A. Schwarz

J. Math. Phys. 51, 015201 (2010); http://dx.doi.org/10.1063/1.3257623 (7 pages) | Cited 3 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Show PACS
11.25.Sq Nonperturbative techniques; string field theory
11.30.Pb Supersymmetry
02.40.-k Geometry, differential geometry, and topology
11.10.-z Field theory

Nonequilibrium, thermostats, and thermodynamic limit

G. Gallavotti and E. Presutti

J. Math. Phys. 51, 015202 (2010); http://dx.doi.org/10.1063/1.3257618 (32 pages) | Cited 2 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The relation between thermostats of “isoenergetic” and “frictionless” kind is studied and their equivalence in the thermodynamic limit is proven in space dimension d = 1,2 and for special geometries, d = 3.
Show PACS
05.70.Ln Nonequilibrium and irreversible thermodynamics
05.70.Ce Thermodynamic functions and equations of state

Time asymptotics and entanglement generation of Clifford quantum cellular automata

Johannes Gütschow, Sonja Uphoff, Reinhard F. Werner, and Zoltán Zimborás

J. Math. Phys. 51, 015203 (2010); http://dx.doi.org/10.1063/1.3278513 (35 pages) | Cited 3 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We consider Clifford quantum cellular automata (CQCAs) and their time-evolution. CQCAs are an especially simple type of quantum cellular automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs, and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, such as quasifree and stabilizer states. Finally, we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.
Show PACS
03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
03.67.Lx Quantum computation architectures and implementations
02.60.-x Numerical approximation and analysis
05.45.Df Fractals

Landau damping

C. Mouhot and C. Villani

J. Math. Phys. 51, 015204 (2010); http://dx.doi.org/10.1063/1.3285283 (7 pages) | Cited 10 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
In this note we present the main results from the recent work of Mouhot and Villani (“On the Landau damping,” arXiv:0904.2760) , which for the first time establish Landau damping in a nonlinear context.
Show PACS
52.65.Ff Fokker-Planck and Vlasov equation

Singularities of complex-valued solutions of the two-dimensional Burgers system

Dong Li and Yakov G. Sinai

J. Math. Phys. 51, 015205 (2010); http://dx.doi.org/10.1063/1.3276099 (16 pages) | Cited 5 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We consider the two-dimensional viscous Burgers system without external forcing. For complex-valued solutions, due to the loss of maximum principle and energy estimates, smooth solutions can develop finite-time singularities. We construct an open set of six-parameter families of initial conditions such that the corresponding solutions exhibit blowups in finite time.
Show PACS
47.10.ad Navier-Stokes equations

Hard-sphere fluids with chemical self-potentials

M. K.-H. Kiessling and J. K. Percus

J. Math. Phys. 51, 015206 (2010); http://dx.doi.org/10.1063/1.3279598 (42 pages) | Cited 1 time

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The existence, uniqueness, and stability of solutions are studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container math ⊂ math3 and in contact with either a heat and a matter reservoir, or just a heat reservoir. The local thermodynamics is furnished by the statistical mechanics of a system of hard balls, in the approximation of Carnahan–Starling. The fluid’s local chemical potential per particle at r ∊ Λ is the sum of the matter reservoir’s contribution and a self-contribution −(V∗ρ)(r), where ρ is the fluid density function and V a non-negative linear combination of the Newton kernel VN(|r|) = −|r|−1, the Yukawa kernel VY(|r|) = −|r|−1e−κ|r|, and a van der Waals kernel VW(|r|) = −(1+ϰ2|r|2)−3. The fixed point equations involving the Yukawa and Newton kernels are equivalent to semilinear elliptic partial differential equations (PDEs) of second order with a nonlinear, nonlocal boundary condition. We prove the existence of a grand canonical phase transition and of a petit canonical phase transition which is embedded in the former. The proofs suggest that, except for boundary layers, the grand canonical transition is of the type “all gas↔all liquid” while the petit canonical one is of the type “all vapor↔liquid drop with vapor atmosphere.” The latter proof, in particular, suggests the existence of solutions with interface structure which compromise between the all-liquid and all-gas density solutions.
Show PACS
65.20.-w Thermal properties of liquids
64.70.F- Liquid-vapor transitions
61.20.-p Structure of liquids

Quasiperiodic motions in dynamical systems: Review of a renormalization group approach

Guido Gentile

J. Math. Phys. 51, 015207 (2010); http://dx.doi.org/10.1063/1.3271653 (34 pages) | Cited 2 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasiperiodic solutions the issue of convergence of the series is bedeviled by the so-called small divisor problem. In this paper we review a method recently introduced to deal with such a problem, based on renormalization group ideas and multiscale techniques. Applications to both quasi-integrable Hamiltonian systems [Kolmogorov-Arnold-Moser (KAM) theory] and non-Hamiltonian dissipative systems are discussed. The method is also suited to situations in which the perturbation series diverges and a resummation procedure can be envisaged, leading to a solution which is not analytic in the perturbation parameter: we consider explicitly examples of solutions which are only C∞ in the perturbation parameter, or even defined on a Cantor set.
Show PACS
11.10.Gh Renormalization
02.30.Lt Sequences, series, and summability
02.30.Hq Ordinary differential equations

A quantum central limit theorem for sums of independent identically distributed random variables

V. Jakšić, Y. Pautrat, and C.-A. Pillet

J. Math. Phys. 51, 015208 (2010); http://dx.doi.org/10.1063/1.3285287 (8 pages) | Cited 2 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We formulate and prove a general central limit theorem for sums of independent identically distributed noncommutative random variables.
Show PACS
03.65.Fd Algebraic methods
02.30.Tb Operator theory
02.50.Cw Probability theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

From operator algebras to superconformal field theory

Yasuyuki Kawahigashi

J. Math. Phys. 51, 015209 (2010); http://dx.doi.org/10.1063/1.3285045 (20 pages) | Cited 1 time

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Show PACS
11.10.Nx Noncommutative field theory
02.30.Tb Operator theory
11.30.Pb Supersymmetry
11.25.Hf Conformal field theory, algebraic structures
02.10.Ud Linear algebra

Twenty five years of two-dimensional rational conformal field theory

Jürgen Fuchs, Ingo Runkel, and Christoph Schweigert

J. Math. Phys. 51, 015210 (2010); http://dx.doi.org/10.1063/1.3277118 (19 pages) | Cited 6 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
A review for the 50th anniversary of the Journal of Mathematical Physics.
Show PACS
11.25.Hf Conformal field theory, algebraic structures
11.27.+d Extended classical solutions; cosmic strings, domain walls, texture
11.25.Uv D branes
11.15.Ha Lattice gauge theory
11.15.Yc Chern-Simons gauge theory

Exact results for ionization of model atomic systems

O. Costin, J. L. Lebowitz, C. Stucchio, and S. Tanveer

J. Math. Phys. 51, 015211 (2010); http://dx.doi.org/10.1063/1.3280951 (16 pages) | Cited 2 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We review recent rigorous results concerning the ionization of model quantum systems by time-periodic external fields. The systems we consider consist of a single particle (electron) with a reference Hamiltonian H0 = −Δ+V0(x) (x ∊ mathd) having both bound and continuum states. Starting from an initially localized state ψ0(x) ∊ L2(mathd), the system is subjected for t ≥ 0 to an arbitrary strength time-periodic potential V1(x,t) = V1(x,t+2π/ω). We prove that for a large class of V0(x) and V1(x,t), the wave function ψ(x,t) will delocalize as t→∞, i.e., the system will ionize. The only exceptions are cases where there are time-periodic bound states of the Floquet operator associated with H0+V1. These do occur (albeit rarely) when V1 is not small. For spatially rapidly decaying V0 and V1, ψ(x,t) is generally given, for very long times, by a power series in t−1/2 which we prove in some cases to be Borel summable. For the Coulomb potential V0(x) = −b|x|−1 in math3, we prove ionization for V1(x,t) = V1(|x|)sin(ωt−θ), V1(|x|) = 0 for |x|>R and V1(x)>0 for |x| ≤ R. For this model, if ψ0 is compactly supported both in x and in angular momentum, L, we obtain that ψ(x,t) ∼ O(t−5/6) as t→∞.
Show PACS
03.65.Ge Solutions of wave equations: bound states
34.50.Gb Electronic excitation and ionization of molecules

Developments in the theory of universality

Vieri Mastropietro

J. Math. Phys. 51, 015212 (2010); http://dx.doi.org/10.1063/1.3274807 (18 pages) | Cited 1 time

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Recently, a rigorous foundation of several aspects of the theory of universality for statistical mechanics models with continuously varying exponents (among which are interacting planar Ising models, quantum spin chains, and one-dimensional Fermi systems) has been reached; it has its root in the mapping of such systems into fermionic interacting theories and uses the modern renormalization group methods developed in the context of constructive quantum field theory. No use of exact solutions is done and the analysis applies either to solvable or not solvable models. A review of such developments will be given here.
Show PACS
75.10.Jm Quantized spin models, including quantum spin frustration
11.10.Hi Renormalization group evolution of parameters
05.30.Fk Fermion systems and electron gas

Batalin–Vilkovisky integrals in finite dimensions

C. Albert, B. Bleile, and J. Fröhlich

J. Math. Phys. 51, 015213 (2010); http://dx.doi.org/10.1063/1.3278524 (31 pages) | Cited 1 time

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The Batalin–Vilkovisky (BV) method is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological perturbation theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat–Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.
Show PACS
11.15.Bt General properties of perturbation theory
02.30.Rz Integral equations

Almost commuting matrices, localized Wannier functions, and the quantum Hall effect

Matthew B. Hastings and Terry A. Loring

J. Math. Phys. 51, 015214 (2010); http://dx.doi.org/10.1063/1.3274817 (32 pages) | Cited 5 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
For models of noninteracting fermions moving within sites arranged on a surface in three-dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are K-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward and does not require translational invariance or introduce a flux torus. We further show that there is a Z2 index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as time-reversal or particle-hole conjugation. Finally, in the case of the sphere—mathematically speaking, three almost commuting Hermitians whose sum of square is near the identity—we give the first quantitative result, showing that this index is the only obstruction to finding commuting approximations. We review the known nonquantitative results for the torus.
Show PACS
73.43.-f Quantum Hall effects
02.10.Yn Matrix theory
05.30.Fk Fermion systems and electron gas
02.40.-k Geometry, differential geometry, and topology

Algebraic complementarity in quantum theory

Dénes Petz

J. Math. Phys. 51, 015215 (2010); http://dx.doi.org/10.1063/1.3276681 (11 pages) | Cited 2 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
This paper is an overview of the concept of complementarity, the relation to state estimation, to Connes–Størmer conditional (or relative) entropy, and to uncertainty relation. Complementary Abelian and noncommutative subalgebras are analyzed. All the known results about complementary decompositions are described and several open questions are included. The paper contains only few proofs, typically references are given.
Show PACS
03.65.Fd Algebraic methods
03.65.Ta Foundations of quantum mechanics; measurement theory
02.10.Ud Linear algebra
03.67.-a Quantum information

Spectral gap, and split property in quantum spin chains

Taku Matsui

J. Math. Phys. 51, 015216 (2010); http://dx.doi.org/10.1063/1.3285046 (8 pages) | Cited 1 time

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
In this article, we consider a class of ground states with spectral gap for quantum spin chains on an integer lattice and we prove that the factorization lemma of Hastings [“Topology and phases in fermionic systems,” J. Stat. Mech.: Theory Exp. 2008, L01001 ] implies split property (weak statistical independence) of left and right semi-infinite subsystems.
Show PACS
03.65.Fd Algebraic methods
75.10.Pq Spin chain models
75.10.Jm Quantized spin models, including quantum spin frustration
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.10.Yn Matrix theory
02.30.Cj Measure and integration

Statics and dynamics of magnetic vortices and of Nielsen–Olesen (Nambu) strings

S. Gustafson, I. M. Sigal, and T. Tzaneteas

J. Math. Phys. 51, 015217 (2010); http://dx.doi.org/10.1063/1.3280039 (16 pages) | Cited 7 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We review recent works on statics and dynamics of magnetic vortices in the Ginzburg–Landau model of superconductivity and of Nielsen–Olesen (Nambu) strings in the Abelian–Higgs model of particle physics.
Show PACS
74.25.Ha Magnetic properties including vortex structures and related phenomena
74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.)
11.25.-w Strings and branes

The principle of locality: Effectiveness, fate, and challenges

Sergio Doplicher

J. Math. Phys. 51, 015218 (2010); http://dx.doi.org/10.1063/1.3276100 (20 pages) | Cited 1 time

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its “unreasonable effectiveness” in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical formulation to the measurement process in local and relativistic terms; for which we outline a qualitative scenario which avoids the Einstein, Podolski, and Rosen paradox.
Show PACS
03.30.+p Special relativity
04.20.Gz Spacetime topology, causal structure, spinor structure
04.50.-h Higher-dimensional gravity and other theories of gravity
11.10.-z Field theory

Rigorous meaning of McLennan ensembles

Christian Maes and Karel Netočný

J. Math. Phys. 51, 015219 (2010); http://dx.doi.org/10.1063/1.3274819 (16 pages) | Cited 4 times

Online Publication Date: 29 January 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We analyze the exact meaning of expressions for nonequilibrium stationary distributions in terms of entropy changes. They were originally introduced by McLennan [“Statistical mechanics of the steady state,” Phys. Rev. 115, 1405 (1959)] for mechanical systems close to equilibrium and more recent work by Komatsu and Nakagawa [“An expression for stationary distribution in nonequilibrium steady states,” Phys. Rev. Lett. 100, 030601 (2008)] has shown their intimate relation to the transient fluctuation symmetry. Here we derive these distributions for jump and diffusion Markov processes and we clarify the order of the limits that take the system both to its stationary regime and to the close-to-equilibrium regime. In particular, we prove that it is exactly the (finite) transient component of the irreversible part of the entropy flux that corrects the Boltzmann distribution to first order in the driving. We add further connections with the notion of local equilibrium, with the Green–Kubo relation, and with a generalized expression for the stationary distribution in terms of a reference equilibrium process.
Show PACS
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.Ga Markov processes
05.70.Ce Thermodynamic functions and equations of state
05.60.-k Transport processes
Close

Google Calendar

ADVERTISEMENT

Go to AIP Home   © AIP Publishing LLC
close