In the last 30 days

• Open/close Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems

  M Daoud and M R Kibler  2010 J. Phys. A: Math. Theor. 43 115303 Tag this article

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  We introduce a one-parameter-generalized oscillator algebra (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter κ. We define an (Hamiltonian) operator associated with and examine the degeneracies of its spectrum. For the finite (when κ < 0) and the infinite (when κ ≥ 0) representations of , we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators. To overcome the difficulties related to the phase operator in the infinite-dimensional case and to avoid the degeneracy problem for the finite-dimensional case, we introduce a truncation procedure which generalizes the one used by Pegg and Barnett for the harmonic oscillator. This yields a truncated-generalized oscillator algebra , where s denotes the truncation order. We construct two types of temporally stable states for (as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of ). Two applications are considered in this paper. The first concerns physical realizations of and in the context of one-dimensional quantum systems with finite (Morse system) or infinite (Pöschl–Teller system) discrete spectra. The second deals with mutually unbiased bases used in quantum information.

• Open/close Entanglement in continuous-variable systems: recent advances and current perspectives

  Gerardo Adesso and Fabrizio Illuminati  2007 J. Phys. A: Math. Theor. 40 7821 Tag this article

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  We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states. Multipartite entanglement of Gaussian states is reviewed by discussing its qualification by different classes of separability, and the main consequences of the monogamy inequality, such as the quantification of genuine tripartite entanglement in three-mode Gaussian states, the promiscuous nature of entanglement sharing in symmetric Gaussian states and the possible coexistence of unlimited bipartite and multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non-Gaussian states, a field of research that is to a large extent yet to be explored.

• Open/close A direct method for solving the generalized sine-Gordon equation

  Yoshimasa Matsuno  2010 J. Phys. A: Math. Theor. 43 105204 Tag this article

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  The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method. In particular, we construct multisoliton solutions in the form of parametric representation. We obtain a variety of solutions which include kinks, loop solitons and breathers. The properties of these solutions are investigated in detail. We find a novel type of solitons with a peculiar structure that the smaller soliton travels faster than the larger soliton. We also show that the short-pulse equation describing the propagation of ultra-short pulses is reduced from the generalized sG equation in an appropriate scaling limit. Subsequently, the reduction to the sG equation is briefly discussed.

• Open/close Quantum hydrodynamic models from a maximum entropy principle

  M Trovato and L Reggiani  2010 J. Phys. A: Math. Theor. 43 102001 Tag this article

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  We use a density matrix formalism to derive a kinetic theory for a quantum gas. Generalized kinetic fields are introduced and, employing the Wigner function, a certain hierarchy of quantum hydrodynamic (QHD) equations for the corresponding macroscopic variables is obtained. We assert a maximum entropy principle to obtain closure of the QHD system. For the explicit incorporation of statistics a proper quantum entropy is analyzed in terms of the reduced density matrix. The determination of the reduced Wigner function for equilibrium and non-equilibrium conditions is found to become possible only by assuming that the Lagrange multipliers can be expanded in powers of ². Quantum contributions are expressed in powers of ² while classical results are recovered in the limit → 0.

• Open/close The quantum effective mass Hamilton–Jacobi problem

  Özlem Yeşiltaş  2010 J. Phys. A: Math. Theor. 43 095305 Tag this article

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  In this paper, the quantum Hamilton–Jacobi theory based on the position-dependent mass model is studied. Two effective mass functions having different singularity structures are used to examine the Morse and Pöschl–Teller potentials. The residue method is used to obtain the solutions of the quantum effective mass- Hamilton–Jacobi equation. Further, it is shown that the eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and Pöschl–Teller potentials can be obtained by using the Riccati equation without solving a differential equation.

• Open/close Uniqueness theorem for an inverse scattering problem with non-overdetermined data

  A G Ramm  2010 J. Phys. A: Math. Theor. 43 112001 Tag this article

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  Let q( x) be a real-valued compactly supported sufficiently smooth function. It is proved that the scattering data A(− β, β, k) ∀β S ², ∀ k > 0 determine q uniquely.

• Open/close A short review on entanglement in quantum spin systems

  J I Latorre and A Riera  2009 J. Phys. A: Math. Theor. 42 504002 Tag this article

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  We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.

• Open/close Time-dependent focusing billiards and macroscopic realization of Maxwell's Demon

  A B Ryabov and A Loskutov  2010 J. Phys. A: Math. Theor. 43 125104 Tag this article

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  The Fermi acceleration is always inherent in completely chaotic time-dependent billiards. At the same time, the particle dynamics in nearly integrable billiard systems can be more complex. Using a simplified approach, we investigate time-dependent stadium-like billiards and show that at a certain particle velocity, V _r, a resonance between external periodical perturbations and the motion within stability islands of the unperturbed billiard can be observed. This resonance suppresses the Fermi acceleration of particles with velocities less than V _r. As a result, we observe a separation of billiard particles by their velocities. If V ₀ < V _r, the average particle velocity decreases, while the particles with V ₀ > V _r are on average accelerated. At the initial velocity V ₀ = V _r we observe a phase transition in the velocity distribution of particles: if V ₀ < V _r then the distribution approaches a stationary one, whereas for V ₀ > V _r the distribution is non-stationary and spreads toward the higher velocities. This phenomenon may be treated as a peculiar billiard Maxwell's Demon, when weak perturbations of a system lead the particle ensemble to separation. In other nearly integrable billiard systems similar resonances can lead to differences in the acceleration of particles with velocities smaller or larger than a resonance value.

• Open/close Time at which the maximum of a random acceleration process is reached

  Satya N Majumdar et al  2010 J. Phys. A: Math. Theor. 43 115001 Tag this article

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  We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the probability density p( t _m| T) of the time t _m at which the process reaches its maximum, within a fixed time interval [0, T]. We study two different boundary conditions, which correspond to the process representing respectively (i) the integral of a Brownian bridge and (ii) the integral of a free Brownian motion. Our analytical results are also verified by numerical simulations.

• Open/close Conformal self-dual fields

  R R Metsaev  2010 J. Phys. A: Math. Theor. 43 115401 Tag this article

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  Conformal self-dual fields in flat spacetime of even dimension greater than or equal to 4 are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained. Gauge symmetries are realized by involving the Stueckelberg fields. The realization of global conformal symmetries is obtained. The light-cone gauge Lagrangian is found. Also, we demonstrate the use of the light-cone gauge for counting the on-shell degrees of freedom of the conformal self-dual fields.