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Jan 2007

Volume 48, Issue 1, Articles (01xxxx)

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Strong-coupling limit for the ground state of a particle harmonic oscillator interaction

Holly Carley

J. Math. Phys. 48, 012101 (2007); http://dx.doi.org/10.1063/1.2400829 (13 pages)

Online Publication Date: 3 January 2007

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We consider the quantum Hamiltonian for a particle interacting with a harmonic oscillator, H ≔ −Δx+A†A+λϕA+λϕ*A†, for various choices of coupling potential ϕ = ϕ(x), where A† and A are creation and annihilation operators, and λ is a parameter to be thought of as large. This operator is a caricature of the polaron Hamiltonian where the quantum field is approximated by a single mode. The large λ corresponds to large coupling between the electron and the field. Let E0(λ) be the infimum of the spectrum of H, and let EP(λ) = inf〈ψ,Hψ〉 where the infimum is taken over product states for the electron and oscillator, the oscillator function taken as a coherent state. It is a remarkable fact that EP(λ) is a “good” approximation of E0(λ). More specifically, (EP(λ)−1) ⩽ E0(λ) ⩽ EP(λ) for all λ, as observed by Lieb. In this paper we examine this gap EP(λ)−E0(λ) for various choices of ϕ, showing cases where it closes and cases where it does not.
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03.65.Ge Solutions of wave equations: bound states
03.65.Fd Algebraic methods
71.38.-k Polarons and electron-phonon interactions
02.10.Ud Linear algebra

Canonical coset parametrization and the Bures metric of the three-level quantum systems

S. J. Akhtarshenas

J. Math. Phys. 48, 012102 (2007); http://dx.doi.org/10.1063/1.2405401 (12 pages) | Cited 3 times

Online Publication Date: 4 January 2007

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An explicit parametrization for the state space of an n-level density matrix is given. The parametrization is based on the canonical coset decomposition of unitary matrices. We also compute, explicitly, the Bures metric tensor over the state space of two- and three-level quantum systems.
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03.65.Fd Algebraic methods
02.10.Yn Matrix theory
02.10.Ud Linear algebra

Extended weak coupling limit for Friedrichs Hamiltonians

Jan Dereziński and Wojciech De Roeck

J. Math. Phys. 48, 012103 (2007); http://dx.doi.org/10.1063/1.2405402 (19 pages) | Cited 1 time

Online Publication Date: 5 January 2007

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We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a “small subsystem” and an infinite dimensional one called a “reservoir.” The operator, which we call a “Friedrichs Hamiltonian,” has a small coupling constant in front of its off-diagonal term. It is well known that under some conditions in the weak coupling limit the appropriately rescaled evolution in the interaction picture converges to a contractive semigroup when restricted to the subsystem. We show that in this model, the properly renormalized and rescaled evolution converges on the whole space to a new unitary evolution, which is a dilation of the above mentioned semigroup. Similar results have been studied before ( Accardi et al., 1990 ) in more complicated models under the name of “stochastic limit.”
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03.65.Fd Algebraic methods
02.20.-a Group theory
02.30.Tb Operator theory

On Weyl channels being covariant with respect to the maximum commutative group of unitaries

Grigori G. Amosov

J. Math. Phys. 48, 012104 (2007); http://dx.doi.org/10.1063/1.2406054 (14 pages)

Online Publication Date: 10 January 2007

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We investigate the Weyl channels being covariant with respect to the maximum commutative group of unitary operators. This class includes the quantum depolarizing channel and the “two-Pauli” channel as well. Then, we show that our estimation of the output entropy for a tensor product of the phase damping channel and the identity channel based upon the decreasing property of the relative entropy allows to prove the additivity conjecture for the minimal output entropy for the quantum depolarizing channel in any prime dimension and for the two-Pauli channel in the qubit case.
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03.65.Fd Algebraic methods
03.67.-a Quantum information
02.20.Uw Quantum groups

Quasiseparation of variables in the Schrödinger equation with a magnetic field

F. Charest, C. Hudon, and P. Winternitz

J. Math. Phys. 48, 012105 (2007); http://dx.doi.org/10.1063/1.2399087 (16 pages) | Cited 3 times

Online Publication Date: 22 January 2007

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We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the separation of variables in the Schrödinger equation. We introduce the concept of “quasiseparation of variables” and show that in many cases it allows us to reduce the calculation of the energy spectrum and wave functions to linear algebra.
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03.65.Ge Solutions of wave equations: bound states
03.65.Fd Algebraic methods
02.10.Ud Linear algebra
02.30.Ik Integrable systems

Quantum dynamical semigroups for finite and infinite Bose systems

Ph. Blanchard, M. Hellmich, P. Ługiewicz, and R. Olkiewicz

J. Math. Phys. 48, 012106 (2007); http://dx.doi.org/10.1063/1.2406053 (12 pages) | Cited 3 times

Online Publication Date: 29 January 2007

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A new class of quasifree quantum Markov semigroups on C*-algebras of canonical commutation relations is introduced and discussed. Two applications to decoherence in the Heisenberg representation are given. In the first one the dynamical semigroup which leads to the appearance of decoherence induced superselection rules corresponding to the boundary conditions of a quantum particle in a finite interval is considered. The second example analyzes the possibility of the transition from infinite systems to systems with a finite number of degrees of freedom.
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03.65.Fd Algebraic methods
02.20.Uw Quantum groups
02.50.Ga Markov processes

Complementary reductions for two qubits

Dénes Petz and Jonas Kahn

J. Math. Phys. 48, 012107 (2007); http://dx.doi.org/10.1063/1.2424883 (6 pages) | Cited 2 times

Online Publication Date: 30 January 2007

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Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A1,A2,…,Ak are pairwise complementary (or quasiorthogonal) subalgebras of the algebra M4(math) of all 4×4 matrices and they are isomorphic to M2(math), then k ⩽ 4. The proof is based on a Cartan decomposition of SU(4). In the way to the main result, contributions are made to the understanding of the structure of complementary reductions.
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03.67.Lx Quantum computation architectures and implementations
02.10.Yn Matrix theory

Dual monogamy inequality for entanglement

Gilad Gour, Somshubhro Bandyopadhyay, and Barry C. Sanders

J. Math. Phys. 48, 012108 (2007); http://dx.doi.org/10.1063/1.2435088 (13 pages) | Cited 13 times

Online Publication Date: 31 January 2007

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We establish duality for monogamy of entanglement: whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, as quantified by linear entropy, we prove that the same quantity (namely, linear entropy) provides a lower bound for distribution of bipartite entanglement in a multipartite system. Our theorem for monogamy of entanglement is used to establish relations between bipartite entanglement that separate one qubit from the rest versus separating two qubits from the rest.
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03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
03.67.Mn Entanglement measures, witnesses, and other characterizations
03.67.Lx Quantum computation architectures and implementations

Features of Moyal trajectories

Nuno Costa Dias and João Nuno Prata

J. Math. Phys. 48, 012109 (2007); http://dx.doi.org/10.1063/1.2409495 (23 pages) | Cited 5 times

Online Publication Date: 31 January 2007

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We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that this divergence is quite general by studying Hamiltonians of the form p2/2m+V(q). Several alternative formulations of Moyal dynamics are then suggested. We introduce the concept of star function and use it to reformulate the Moyal equations in terms of a system of ordinary differential equations on the noncommutative Moyal plane. We then use this formulation to study the semiclassical expansion of Moyal trajectories, which is cast in terms of a (order by order in ℏ) recursive hierarchy of (i) first order partial differential equations as well as (ii) systems of first order ordinary differential equations. The latter formulation is derived independently for analytic Hamiltonians as well as for the more general case of locally integrable ones. We present various examples illustrating these results.
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03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Sq Semiclassical theories and applications
02.30.Jr Partial differential equations

Degenerate discrete energy spectra and associated coherent states

L. Dello Sbarba and V. Hussin

J. Math. Phys. 48, 012110 (2007); http://dx.doi.org/10.1063/1.2435596 (15 pages) | Cited 1 time

Online Publication Date: 31 January 2007

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Generalized and Gaussian coherent states constructed for quantum system with degeneracies in the energy spectrum are compared with respect to some minimal definitions and fundamental properties they have to satisfy. The generalized coherent states must be eigenstates of a certain annihilation operator that has to be properly defined in the presence of degeneracies. The Gaussian coherent states are, in the particular harmonic oscillator case, an approximation of the generalized coherent states and so the localizability in phase space of the particle in those states is very good. For other quantum systems, this last property serves as a definition of those Gaussian coherent states. The example of a particle in a two-dimensional square box is thus revisited having in mind the preceding definitions of generalized and Gaussian coherent states and also the preservation of the important property known as the resolution of the identity operator.
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03.65.Ge Solutions of wave equations: bound states
02.10.Ud Linear algebra

Finite size effects in bistable ϕ4 models

Marco Zoli

J. Math. Phys. 48, 012111 (2007); http://dx.doi.org/10.1063/1.2435601 (14 pages) | Cited 1 time

Online Publication Date: 31 January 2007

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The work proposes a finite temperature theory of the quantum tunneling in a bistable quartic potential. In semiclassical approximation, the imaginary time path integral method identifies the classical background which interpolates between the potential minima and, at any T, consistently fulfills antiperiodic boundary conditions. Solving the boundary problem I find that the change between the low T quantum regime and the high T activated regime exhibits the signatures of a first order phase transition. This is confirmed by the discontinuity in the first temperature derivative of the instantonic action. The quantum fluctuation contribution around the (anti)instantons is evaluated by the functional determinant method. The computation of the tunneling energy shows (i) a remarkable reduction at low T with respect to the predictions of the infinite size canonical instantonic approach, and (ii) a steplike increase at the transition point.
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11.10.Wx Finite-temperature field theory
11.15.-q Gauge field theories
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
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Hidden geometric character of relativistic quantum mechanics

José B. Almeida

J. Math. Phys. 48, 012301 (2007); http://dx.doi.org/10.1063/1.2406055 (14 pages)

Online Publication Date: 11 January 2007

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Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4×4 matrices, also known as Dirac’s matrices. There is one problem with this isomorphism, because the solutions to Dirac’s equation are usually known as spinors (column matrices) that do not belong to the 4×4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive∕negative energy together with left∕right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.
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03.65.Ge Solutions of wave equations: bound states
03.30.+p Special relativity
03.65.Pm Relativistic wave equations
04.20.Gz Spacetime topology, causal structure, spinor structure
02.40.-k Geometry, differential geometry, and topology
02.10.-v Logic, set theory, and algebra

Large N behavior of two dimensional supersymmetric Yang-Mills quantum mechanics

Maciej Trzetrzelewski

J. Math. Phys. 48, 012302 (2007); http://dx.doi.org/10.1063/1.2408399 (16 pages) | Cited 4 times

Online Publication Date: 17 January 2007

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We analyze the N→∞ limit of supersymmetric Yang-Mills quantum mechanics (SYMQM) in two space time dimensions. To do so we introduce a particular class of SU(N) invariant polynomials and give the solutions of two-dimensional SYMQM in terms of them. We conclude that in this limit the system is not fully described by the single trace operators Tr(a†n) since there are other, bilinear operators Trn(a†a†) that play a crucial role when the Hamiltonian is free.
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11.15.-q Gauge field theories
11.30.Pb Supersymmetry
11.30.Ly Other internal and higher symmetries
11.10.Ef Lagrangian and Hamiltonian approach

Lorentzian version of the noncommutative geometry of the standard model of particle physics

John W. Barrett

J. Math. Phys. 48, 012303 (2007); http://dx.doi.org/10.1063/1.2408400 (7 pages) | Cited 17 times

Online Publication Date: 26 January 2007

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A formulation of the noncommutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian case is achieved by a modification of Connes’ internal space geometry [ “Gravity coupled with matter and the foundation of non-commutative geometry,” Commun. Math. Phys. 182, 155–176 (1996) ] so that it has signature 6 (mod 8) rather than 0. The fermionic part of the Connes-Chamseddine spectral action can be formulated, and it is shown that it allows an extension with right-handed neutrinos and the correct mass terms for the seesaw mechanism of neutrino mass generation.
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11.10.Nx Noncommutative field theory
12.10.-g Unified field theories and models
14.60.Pq Neutrino mass and mixing
02.40.Gh Noncommutative geometry

Note on math2 symmetries of the Knizhnik-Zamolodchikov equation

Gaston E. Giribet

J. Math. Phys. 48, 012304 (2007); http://dx.doi.org/10.1063/1.2424789 (19 pages) | Cited 2 times

Online Publication Date: 26 January 2007

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We continue the study of hidden math2 symmetries of the four-point mathk Knizhnik-Zamolodchikov equation initiated by Giribet [Phys. Lett. B 628, 148 (2005) ]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector ω = 1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed states. This means that the formula holding for the winding violating four-string scattering processes in AdS3 has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of three-point functions, where the violating and the nonviolating structure constants turn out to be connected one to each other in a similar way. What makes this connection particularly simple is the fact that, unlike what one would naively expect, it is not necessary to explicitly solve the five-point function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the Knizhnik-Zamolodchikov equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it is not sufficient; besides, the formula also follows from the relation existing between correlators in both Wess-Zumino-Novikov-Witten (WZNW) and Liouville conformal theories.
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11.27.+d Extended classical solutions; cosmic strings, domain walls, texture
11.25.Hf Conformal field theory, algebraic structures
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Multipole structure of current vectors in curved space-time

Abraham I. Harte

J. Math. Phys. 48, 012501 (2007); http://dx.doi.org/10.1063/1.2409526 (19 pages) | Cited 1 time

Online Publication Date: 23 January 2007

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A method is presented which allows the exact construction of conserved (i.e., divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric charge inside some classical extended body. Several applications are discussed. In particular, it is shown how to easily write down the class of all smooth and spatially bounded currents with a given total charge. This implicitly provides restrictions on the moments arising from the smoothness of physically reasonable vector fields. We also show that requiring all of the moments to be constant in an appropriate sense is often impossible. This likely limits the applicability of the Ehlers-Rudolph-Dixon notion of quasirigid motion. A simple condition is also derived that allows currents to exist in two different space-times with identical sets of multipole moments (in a natural sense).
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04.20.Gz Spacetime topology, causal structure, spinor structure
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Incursive discretization, system bifurcation, and energy conservation

Adel F. Antippa and Daniel M. Dubois

J. Math. Phys. 48, 012701 (2007); http://dx.doi.org/10.1063/1.2423225 (9 pages) | Cited 1 time

Online Publication Date: 24 January 2007

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Incursive discretization of the classical harmonic oscillator leads to system bifurcation. The resulting hyperincursive representation has two alternative distinct algorithms of ordered, serial, noncommuting instructions, and admits solutions having a discretized classical total energy that is perfectly conserved and phase space trajectories that are fully stable at all time scales. Hyperincursive representations can be generated for any Hamiltonian system.
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05.45.-a Nonlinear dynamics and chaos

Geometric integration of the electromagnetic two-body problem

Jayme De Luca

J. Math. Phys. 48, 012702 (2007); http://dx.doi.org/10.1063/1.2424551 (10 pages) | Cited 5 times

Online Publication Date: 25 January 2007

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The equations of motion of the two-body problem of Dirac’s electrodynamics of point charges consist of a delay equation for the proton and a delay equation for the electron. These equations involve the third derivative of the charges’s position and have runaway solutions, which make forward numerical integration troublesome. Dirac’s equations of motion are algebraic-delay equations, involving a degenerate linear form of the past accelerations. A Fredholm alternative yields a system of second-order delay equations of motion plus a constraint on the initial segment of trajectory. Here we use the Fredholm constraint as a geometric tool to derive covariant second-order equations of motion in position for backward time integration. We also extend the backward integration scheme to include a generalized version of Dirac’s theory that includes two delays.
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03.50.De Classical electromagnetism, Maxwell equations
02.30.Rz Integral equations

Dynamical behavior for the three-dimensional generalized Hasegawa-Mima equations

Ruifeng Zhang and Boling Guo

J. Math. Phys. 48, 012703 (2007); http://dx.doi.org/10.1063/1.2424559 (11 pages) | Cited 1 time

Online Publication Date: 26 January 2007

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The long time behavior of solution of the three-dimensional generalized Hasegawa-Mima [Phys. Fluids 21, 87 (1978)] equations with dissipation term is considered. The global attractor problem of the three-dimensional generalized Hasegawa-Mima equations with periodic boundary condition was studied. Applying the method of uniform a priori estimates, the existence of global attractor of this problem was proven, and also the dimensions of the global attractor are estimated.
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52.35.We Plasma vorticity
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Kt Drift waves
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
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Massless particles in three-dimensional Lorentzian warped products

Jose L. Cabrerizo, Manuel Fernandez, and Miguel Ortega

J. Math. Phys. 48, 012901 (2007); http://dx.doi.org/10.1063/1.2409522 (12 pages)

Online Publication Date: 18 January 2007

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The model of a massless relativistic particle with curvature-dependent Lagrangian is well known in (d+1)-dimensional Minkowski space. For other gravitational fields less rigid than those with constant (zero) curvature only a few results are known. In this paper, we give a geometric approach in order to solve the field equations associated with that Lagrangian in the setting of an interesting three-dimensional background, namely, a three-dimensional warped product with Lorentzian fibers. When some rigidity conditions are imposed to the fiber (constant Gauss curvature), the trajectories can be totally described. Several examples help us clarify this.
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04.20.Gz Spacetime topology, causal structure, spinor structure
02.40.-k Geometry, differential geometry, and topology

Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion

Ian Marquette and Pavel Winternitz

J. Math. Phys. 48, 012902 (2007); http://dx.doi.org/10.1063/1.2399359 (16 pages) | Cited 12 times

Online Publication Date: 23 January 2007

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We present polynomial Poisson algebras for the eight classical potentials in two-dimensional Euclidian space that separate in Cartesian coordinates and allow a third-order integral of motion. Some of the classical superintegrable potentials do not coincide with quantum ones, but are their singular limits. We show that all bounded trajectories in these potentials are periodic.
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02.10.De Algebraic structures and number theory
02.30.Ik Integrable systems
02.30.Jr Partial differential equations
02.30.Rz Integral equations
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On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree

Farrukh Mukhamedov, Utkir Rozikov, and José F. F. Mendes

J. Math. Phys. 48, 013301 (2007); http://dx.doi.org/10.1063/1.2408398 (14 pages)

Online Publication Date: 16 January 2007

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We consider the Potts model with competing two-step interactions and spin values 1, 2, 3 on a semi-infinite Cayley tree of order 2. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence of three different Gibbs measures associated with translation invariant ground states.
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Fh Phase transitions: general studies

Nonresonant kinetic instabilities of a relativistic plasma in a uniform magnetic field: Longitudinal and transverse mode coupling effects

R. C. Tautz, R. Schlickeiser, and I. Lerche

J. Math. Phys. 48, 013302 (2007); http://dx.doi.org/10.1063/1.2424549 (25 pages) | Cited 12 times

Online Publication Date: 24 January 2007

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The stability properties of relativistic plasmas embedded in a uniform magnetic field are investigated for longitudinal and transverse modes and with coupling effects between these modes. The direction of wave propagation in the plasma is not necessarily either parallel or transverse to the ambient magnetic field. The basic dispersion relation equations are given for arbitrary propagation directions. Detailed examination is focused on perpendicular wave propagation in this paper. The concept of neutral points in wave number space, introduced by Harris [Phys. Rev. Lett. 2, 34 (1959)], is generalized to allow for the inclusion of ion effects and the effects of fluctuating magnetic fields. Starting from the relativistic conductivity tensor, an expansion procedure for low wave frequencies is used to determine the stability properties in the neighborhood of neutral points and in the frequency regime below the ion cyclotron frequency. The bulk plasma properties determine stability or instability but the mode structure is derivable only from a particle kinetic picture, as with Weibel [Phys. Rev. Lett. 2, 83 (1959)] instabilities, and not from a magnetohydrodynamic description. For monoenergetic plasma distribution functions of electrons and ions, as well as for electrons and positrons, numerical examples are given to illustrate the neutral points and the unstable wave number regimes.
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52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.27.Ny Relativistic plasmas
52.25.Gj Fluctuation and chaos phenomena
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

On detailed balance and reversibility of semi-Markov processes and single-molecule enzyme kinetics

Hongyun Wang and Hong Qian

J. Math. Phys. 48, 013303 (2007); http://dx.doi.org/10.1063/1.2432065 (15 pages) | Cited 11 times

Online Publication Date: 31 January 2007

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Semi-Markov processes have found increasing applications in modeling the kinetics of single enzyme molecules. Detailed balance is a widely accepted condition for Markov models of closed chemical systems and well known to be equivalent to the reversibility of a stationary Markov process. We show that for a semi-Markov process detailed balance is only a necessary condition, but not sufficient, for its time reversibility. The statistical independence between the transition direction and the sojourn time is also necessary. We show that the direction-time independence naturally arises from the exit problem of Markov models for enzyme kinetics with detailed balance. Detailed balance and the direction-time independence together are equivalent to the time reversibility of a stationary semi-Markov process. Applications of the present theory to single-molecule enzymology are also presented.
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82.39.Fk Enzyme kinetics
82.37.Np Single molecule reaction kinetics, dissociation, etc.
87.15.R- Reactions and kinetics
87.15.A- Theory, modeling, and computer simulation
82.20.Db Transition state theory and statistical theories of rate constants
02.50.Ga Markov processes
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Total cross section exceeds transport cross section for quantum scattering from hard bodies at low and high wave numbers

W. De Roeck and E. L. Lakshtanov

J. Math. Phys. 48, 013501 (2007); http://dx.doi.org/10.1063/1.2405404 (9 pages) | Cited 1 time

Online Publication Date: 8 January 2007

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The quantum scattering by smooth bodies is considered for small and large values of kd, with k the wave number and d the scale of the body. In both regimes, we prove that the forward scattering exceeds the backscattering. For high k, we need to assume that the body is strictly convex.
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03.65.Nk Scattering theory
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