In the last 30 days

• Open/close Quantum communication through open-ended quantum networks

  Zheng-Da Hu et al 2011 J. Phys. A: Math. Theor. 44 425303 Tag this article

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  We study a one-dimensional fibre-coupled cavity array with an open-end boundary condition, where each cavity is doped with a two-level atom, and obtain explicit expressions for the dynamics evolution of the array with arbitrary number of nodes in the far off-resonant condition. It is shown that distant state transfer and entanglement generation schemes may be implemented through this quantum network and an arbitrary state is transferred with high fidelity for the array with specific number of nodes. The entanglement transfer through both single array and double independent arrays is also examined.

• Open/close Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?

  M V Berry et al 2011 J. Phys. A: Math. Theor. 44 492001 Tag this article

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  Probably not.

• Open/close New quasi-exactly solvable double-well potentials

  Qiong-Tao Xie 2012 J. Phys. A: Math. Theor. 45 175302 Tag this article

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  A new three-parameter family of quasi-exactly solvable double-well potentials is introduced. We show that the solutions of this family of double-well potentials are expressed in terms of the Heun confluent functions. Under a certain parameter condition, some of the bound-state wavefunctions and associated energies can be found exactly in explicit form. In particular, we develop an analytical method to derive the conditions for the energy eigenvalues of the bound states. It is also shown that our analytical results can be applied to construct exact solutions of the nonlinear Schrödinger equation with double-well potentials and spatially localized nonlinearities.

• Open/close Superconformal mechanics

  Sergey Fedoruk et al 2012 J. Phys. A: Math. Theor. 45 173001 Tag this article

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  We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single- and multiparticle systems are covered.

• Open/close Efficiency of a Brownian information machine

  Michael Bauer et al 2012 J. Phys. A: Math. Theor. 45 162001 Tag this article

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  A Brownian information machine extracts work from a heat bath through a feedback process that exploits the information acquired in a measurement. For the paradigmatic case of a particle trapped in a harmonic potential, we determine how power and efficiency for two variants of such a machine operating cyclically depend on the cycle time and the precision of the positional measurements. Controlling only the center of the trap leads to a machine that has zero efficiency at maximum power, whereas additional optimal control of the stiffness of the trap leads to an efficiency bounded between 1/2, which holds for maximum power, and 1 reached even for finite cycle time in the limit of perfect measurements.

• Open/close Order in de Broglie–Bohm quantum mechanics

  G Contopoulos et al 2012 J. Phys. A: Math. Theor. 45 165301 Tag this article

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  A usual assumption in the so-called de Broglie–Bohm approach to quantum dynamics is that the quantum trajectories subject to typical ‘guiding’ wavefunctions turn to be quite irregular, i.e. chaotic (in the dynamical systems’ sense). In this paper, we consider mainly cases in which the quantum trajectories are ordered, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a Hénon–Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie–Bohm formalism, namely the influence of order on the so-called quantum relaxation effect. We show that the existence of regular trajectories poses restrictions on the quantum relaxation process and give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.

• Open/close Critical properties of joint spin and Fortuin–Kasteleyn observables in the two-dimensional Potts model

  Romain Vasseur and Jesper Lykke Jacobsen 2012 J. Phys. A: Math. Theor. 45 165001 Tag this article

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  The two-dimensional Potts model can be studied either in terms of the original Q-component spins or in the geometrical reformulation via Fortuin–Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by construction, it was only shown very recently that the spin representation can be promoted to the same level of generality. In this paper we show how to define the Potts model in terms of observables that simultaneously keep track of the spin and FK degrees of freedom. This is first done algebraically in terms of a transfer matrix that couples three different representations of a partition algebra. Using this, one can study correlation functions involving any given number of propagating spin clusters with prescribed colours, each of which contains any given number of distinct FK clusters. For 0 ⩽ Q ⩽ 4, the corresponding critical exponents are all of the Kac form h _{r, s}, with integer indices r, s that we determine exactly both in the bulk and boundary versions of the problem. In particular, we find that the set of points where an FK cluster touches the hull of its surrounding spin cluster has fractal dimension d _{2, 1} = 2 − 2 h _{2, 1}. If one constrains this set to points where the neighbouring spin cluster extends to infinity, we show that the dimension becomes d _{1, 3} = 2 − 2 h _{1, 3}. Our results are supported by extensive transfer matrix and Monte Carlo computations.

• Open/close Algebraic construction of coherent states for nonlinear quantum deformed systems

  A N F Aleixo and A B Balantekin 2012 J. Phys. A: Math. Theor. 45 165302 Tag this article

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  A nonlinear deformed algebraic theory for quantum confined systems is constructed using a supersymmetric and shape-invariant approach. In the framework of this model, we present a mathematical Barut–Girardello procedure which leads to nonlinear deformed coherent states by the successive application of a deformed raising operator on the ground state of these systems. As an application, we use a simple exponential form for the nonlinearity function to study in detail the mathematical and physical properties of such states and their evolution in time.

• Open/close Langevin unification of fractional motions

  Iddo I Eliazar and Michael F Shlesinger 2012 J. Phys. A: Math. Theor. 45 162002 Tag this article

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  We present a physical Langevin-based theory explaining the emergence and pervasiveness of the following ‘fractional motions’: Brownian motion, Lévy motion, fractional Brownian motion and fractional Lévy motion. A general form of micro-level Langevin dynamics, with infinitely many degrees of freedom, is considered. Transcending from the micro-level to the macro-level the infinitely many degrees of freedom collapse to two characteristic exponents, and the aforementioned fractional motions emerge universally. The exponents categorize the fractional motions and determine their statistical and topological properties. The theory establishes a unified ‘Langevin bedrock’ to fractional motions—which are widely applied prototypical models of random transport in the sciences.

• Open/close Nonlocal symmetries related to Bäcklund transformation and their applications

  S Y Lou et al 2012 J. Phys. A: Math. Theor. 45 155209 Tag this article

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  Starting from nonlocal symmetries related to Bäcklund transformation (BT), many interesting results can be obtained. Taking the well-known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in an elegant and compact form which comes from BT is presented and used to perform research works in two main subjects: the nonlocal symmetry is localized by introducing suitable and simple auxiliary-dependent variables to generate new solutions from old ones and to consider some novel group invariant solutions; some other models both in finite and infinite dimensions are generated under new nonlocal symmetry. The finite-dimensional models are completely integrable in Liouville sense, which are shown equivalent to the results given through the nonlinearization method for Lax pair.