In the last 30 days

• Open/close Classical, quantum and total correlations

  L Henderson and V Vedral 2001 J. Phys. A: Math. Gen. 34 6899 Tag this article

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  We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.

• Open/close Calculation of the Casimir force between similar and dissimilar metal plates at finite temperature

  V S Bentsen et al 2005 J. Phys. A: Math. Gen. 38 9575 Tag this article

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  The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite-temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T = 300 K and T = 350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.

• Open/close The mechanism of stochastic resonance

  R Benzi et al 1981 J. Phys. A: Math. Gen. 14 L453 Tag this article

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  It is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance (peak in the power spectrum) which is absent when either the forcing or the perturbation is absent.

• Open/close Generalized Sommerfeld integral and diffraction in an angle-shaped domain with a radial perturbation

  M A Lyalinov 2005 J. Phys. A: Math. Gen. 38 L707 Tag this article

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  The Sommerfeld integral enabled one to solve various diffraction problems in angle-shaped domains. The basic goal of the present paper is to demonstrate a generalized form of the famous Sommerfeld integral. The kernel of the traditional Sommerfeld integral is replaced by the solution of a scattering problem. The latter hint leads to the possibility of representing solutions for a more general class of diffraction problems in an angle-shaped domain with the radial perturbation of the boundary or (and) with the presence of a radially symmetric refraction index in the stationary wave (Helmholtz) equation. The approach is demonstrated in the simplest situation of diffraction in an angle-shaped domain with the centrally circular (with respect to the angle vertex) perturbation of the perfectly conducting boundary.

• Open/close Exact solution of a 1D asymmetric exclusion model using a matrix formulation

  B Derrida et al 1993 J. Phys. A: Math. Gen. 26 1493 Tag this article

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  Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be solved exactly in the case of open boundaries. Here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices. With this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules. They obtain several explicit forms for these non-commuting matrices which are, in the general case, infinite-dimensional. Their approach allows exact expressions to be derived for the current and density profiles. Finally they discuss briefly two possible generalizations of their results: the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles.

• Open/close Parity measurements, decoherence and spiky Wigner functions

  A M Ozorio de Almeida and O Brodier 2004 J. Phys. A: Math. Gen. 37 L249 Tag this article

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  Notwithstanding radical conceptual differences between classical and quantum mechanics, it is usually assumed that physical measurements concern observables common to both theories. Not so with the eigenvalues (±1) of the parity operator. The effect of such a measurement on a mixture of even and odd states of the harmonic oscillator is akin to separating at a single stroke a pair of shuffled card decks: the result is a set of definite parity, though otherwise mixed. Here we derive the general form of a parity collapsed state, whether pure or mixed. The signature of positive or negative parity is a corresponding spike in the Wigner function which is sharpened by decoherence. We conjecture that states with pure parity always have negative values in their Wigner functions.

• Open/close Generalized PT symmetry and real spectra

  Carl M Bender et al 2002 J. Phys. A: Math. Gen. 35 L467 Tag this article

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  The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of a parameter and complex for others is explained by showing that the matrix elements of H, and hence the secular equation, are real, not only for PT but also for any antiunitary operator A satisfying A ^{2 k} = 1 with k odd. The argument is illustrated by a 2 × 2 matrix Hamiltonian, and two examples of the generalization are given.

• Open/close All teleportation and dense coding schemes

  R F Werner 2001 J. Phys. A: Math. Gen. 34 7081 Tag this article

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  We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert–Schmidt scalar product and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be `tight' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d  ² signals. A general construction procedure for orthonormal bases of unitaries, involving Latin squares and complex Hadamard matrices is also presented.

• Open/close Generalised P-representations in quantum optics

  P D Drummond and C W Gardiner 1980 J. Phys. A: Math. Gen. 13 2353 Tag this article

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  A class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators. These are shown to have practical application to the solution of quantum mechanical master equations. Different representations have different domains of integration, on a complex extension of the usual canonical phase-space. The 'complex P-representation' is the case in which analytic P-functions are defined and normalised on contours in the complex plane. In this case, exact steady-state solutions can often be obtained, even when this is not possible using the Glauber-Sudarshan P-representation. The 'positive P-representation' is the case in which the domain is the whole complex phase-space. In this case the P-function may always be chosen positive, and any Fokker-Planck equation arising can be chosen to have a positive-semidefinite diffusion array. Thus the 'positive P-representation' is a genuine probability distribution. The new representations are especially useful in cases of nonclassical statistics.

• Open/close A comparison of simulated annealing cooling strategies

  Yaghout Nourani and Bjarne Andresen 1998 J. Phys. A: Math. Gen. 31 8373 Tag this article

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  Using computer experiments on a simple three-state system and an NP-complete system of permanents we compare different proposed simulated annealing schedules in order to find the cooling strategy which has the least total entropy production during the annealing process for given initial and final states and fixed number of iterations. The schedules considered are constant thermodynamic speed, exponential, logarithmic, and linear cooling schedules. The constant thermodynamic speed schedule is shown to be the best. We are actually considering two different schedules with constant thermodynamic speed, the original one valid for near-equilibrium processes, and a version based on the natural timescale valid also at higher speeds. The latter one delivers better results, especially in case of fast cooling or when the system is far from equilibrium. Also with the lowest energy encountered during the entire optimization (the best-so-far-energy) as the indicator of merit, constant thermodynamic speed is superior. Finally, we have compared two different estimators of the relaxation time. One estimator is using the second largest eigenvalue of the thermalized form of the transition probability matrix and the other is using a simpler approximation for small deviations from equilibrium. These two different expressions only agree at high temperatures.