Table of contents

In this letter we derive the minimum time needed for any state of a given quantum system to evolve adiabatically into a distinct (orthogonal) state. This problem is relevant to deriving physical limits in quantum computation and quantum information processing. Our result represents an adiabatic analogue to the Margolus–Levitin theorem (Margolus and Levitin 1998 Physica D 120, 188).

For quantum systems described by Schrödinger operators on the half-space the boundary force per unit area and unit energy is topologically quantized provided the Fermi energy lies in a gap of the bulk spectrum. Under this condition it is also equal to the integrated density of states at the Fermi energy.

We study the entanglement cost of the states in the antisymmetric space, which consists of (d − 1) d-dimensional systems. The cost is always log₂(d − 1) ebits when the state is divided into bipartite . Combined with the arguments in [6], additivity of channel capacity of some quantum channels is also shown.

Entangled states play a crucial role in quantum information protocols, thus the dynamical behaviour of entanglement is of great importance. In this letter, we consider a two-mode squeezed vacuum state coupled to one thermal reservoir as a model of an entangled state embedded in an environment. As a criterion for entanglement we use a continuous-variable equivalent of the Peres–Horodecki criterion, namely the Simon criterion. To quantify entanglement we use the logarithmic negativity. We derive a condition, which assures that the state remains entangled in spite of the interaction with the reservoir. Moreover for the case of interaction with vacuum as an environment we show that a state of interest after infinitely long interaction is not only entangled, but also pure. For comparison we also consider a model in which each mode is coupled to its own reservoir.

It was recently suggested by Blythe and Evans that a properly defined steady state normalization factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play the role of fugacities. In analogy with the Lee–Yang description of phase transition of equilibrium systems, they studied the zeros in the complex plane of the normalization factor in order to find phase transitions in nonequilibrium steady states. We show that like for equilibrium systems, the 'densities' associated with the rates are nondecreasing functions of the rates and therefore one can obtain the location and nature of phase transitions directly from the analytical properties of the 'densities'. We illustrate this phenomenon for the asymmetric exclusion process. We actually show that its normalization factor coincides with an equilibrium partition function of a walk model in which the 'densities' have a simple physical interpretation.

Classical motion of complex 1D non-Hermitian Hamiltonian systems is investigated analytically to identify periodic, unbounded and chaotic trajectories. Expressions for the Lyapunov exponent for 1D complex Hamiltonians are derived. Complex potentials and V₂(x) = μx³ are studied in detail and their Lyapunov exponents are obtained analytically. It was found that when μ is complex all the trajectories of V₁ are chaotic with Lyapunov exponent |Im(μ)| and most of the trajectories of V₂ are periodic when μ is pure imaginary. But for other complex values of μ trajectories of V₂ are non-periodic and show infinite oscillations. Unbounded neighbouring trajectories of V₂ show power-law divergence rather than exponential divergence as in the case of V₁.

We extend the definition of generalized parity P, charge-conjugation C and time-reversal T operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular, we show that T P and CT P are the generators of the P-antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian H to admit a P-reflecting symmetry which generates the P-pseudounitary and the P-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the P-unitary evolution of a physical system are also given.

This paper studies Randers metrics on homogeneous Riemannian manifolds. It turns out that we can give a complete description of the invariant Randers metrics on a homogeneous Riemannian manifold as well as the geodesics, the flag curvatures. This result provides a convenient method to construct globally defined Berwald space which is neither Riemannian nor locally Minkowskian and gives another explanation of the example of Bao et al (1999 An Introduction to Riemannian–Finsler Geometry (Berlin: Springer)).

Generalized Z_k-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors.

We discuss the finite version of rigid motions in special relativity. Focusing on the extension of the size of a rigid motion, we investigate the reflexive and transitive properties of rigid motions. We show that rigid rotation of a three-dimensional object is impossible while its rigid translation is possible. It is shown that a two-dimensional plane can rotate rigidly.

We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type generalized Hulthén potential. The Klein–Gordon equation has been solved by using the Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. In many cases of interest, negative and positive energy states have been discussed for different types of complex potentials.

Using the geometry of the infinite isotropic Grassmannian related to the Hirota–Ohta-coupled KP hierarchy, we construct its elementary Bäcklund–Darboux transformations.

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl–Heisenberg group, which can then be thought of as characterizing the dual pair.

Entanglement of the excitonic states in the system of two coupled semiconductor microcrystallites, whose sizes are much larger than the Bohr radius of the exciton in the bulk semiconductor but smaller than the relevant optical wavelength, is quantified in terms of the entropy of entanglement. It is observed that the nonlinear interaction between excitons increases the maximum values of the entropy of entanglement more than that of the linear coupling model. Therefore, a system of two coupled microcrystallites can be used as a good source of entanglement with fixed exciton number. The relationship between the entropy of entanglement and the population imbalance of two microcrystallites is numerically shown and the uppermost envelope function for them is estimated by applying the Jaynes principle.

We analysed quantum version of the game battle of sexes using a general initial quantum state. For a particular choice of initial entangled quantum state it is shown that the classical dilemma of the battle of sexes can be resolved and a unique solution of the game can be obtained.

In this paper we adopt a generic, global and non-entropic approach to the problem of the arrow of time, according to which the arrow of time is a generic, intrinsic and geometrical property of spacetime. We demonstrate that the arrow of time so defined is generic in the sense that any spacetime with physically reasonable properties (e.g. time-orientability and global time) will be endowed with an arrow of time. The only exceptions are very special cases belonging to a subset of zero measure of the set of all possible spacetimes. We also show the dual role played by the energy–momentum tensor in the context of our approach. On one hand, the energy–momentum tensor is the intermediate step that permits us to turn the geometrical time-asymmetry of the universe into a local arrow of time manifested as a time-asymmetric energy flow. On the other hand, the energy–momentum tensor supplies the basis for deducing the time-asymmetry of quantum field theory, posed as an axiom in this theory.