1,721,058 research outputs found
Discrete breathers and negative-temperature states
Full text linkWe explore the statistical behaviour of the discrete nonlinear Schrödinger equation as a test bed for the observation of negative-temperature (i.e. above infinite temperature) states in Bose–Einstein condensates in optical lattices and arrays of optical waveguides. By monitoring the microcanonical temperature, we show that there exists a parameter region where the system evolves towards a state characterized by a finite density of discrete breathers and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process. We also discuss two possible mechanisms for the generation of negative-temperature states in experimental setups, namely, the introduction of boundary dissipations and the free expansion of wavepackets initially in equilibrium at a positive temperature
Entanglement estimation in non-optimal qubit states
Full text linkThis is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordIn the last years, a relationship has been established between the quantum Fisher information (QFI) and quantum entanglement. In the case of two-qubit systems, all pure entangled states can be made useful for sub-shot-noise interferometry while their QFI meets a necessary and sufficient condition (Hyllus et al., 2010). In M-qubit systems, the QFI provides just a sufficient condition in the task of detecting the degree of entanglement of a generic state (Pezzé and Smerzi, 2009). In our work, we show analytically that, for a large class of one-parameter non-optimal two-qubit states, the maximally entangled states are associated with stationary points of the QFI, as a function of such parameter. We show, via numerical simulations, that this scenario is maintained for the generalisation of this class of states to a generic M-qubit system. Furthermore, we suggest a scheme for an interferometer able to detect the entanglement in a large class of two-spin states.QuantERAEuropean Commissio
Geometric microcanonical thermodynamics for systems with first integrals
Full text linkIn the general case of a many-body Hamiltonian system described by an autonomous Hamiltonian H and with K≥0 independent conserved quantities, we derive the microcanonical thermodynamics. Using simple approach, based on differential geometry, we derive the microcanonical entropy and the derivatives of the entropy with respect to the conserved quantities. In such a way, we show that all the thermodynamical quantities, such as the temperature, the chemical potential, and the specific heat, are measured as a microcanonical average of the appropriate microscopic dynamical functions that we have explicitly derived. Our method applies also in the case of nonseparable Hamiltonians, where the usual definition of kinetic temperature, derived by the virial theorem, does not apply. © 2012 American Physical Society
Nonclassical dynamics of Bose-Einstein condensates in an optical lattice in the superfluid regime
Full text linkA condensate in an optical lattice, prepared in the ground state of the superfluid regime, is stimulated first by suddenly increasing the optical lattice amplitude and then, after a waiting time, by abruptly decreasing this amplitude to its initial value. Thus the system is first taken to the Mott regime and then back to the initial superfluid regime. We show that, as a consequence of this nonadiabatic process, the system falls into a configuration far from equilibrium whose superfluid order parameter is described in terms of a particular superposition of Glauber coherent states that we derive. We also show that the classical equations of motion describing the time evolution of this system are inequivalent to the standard discrete nonlinear Schrödinger equations. By numerically integrating such equations with several initial conditions, we show that the system loses coherence, becoming insulating. © 2007 The American Physical Society
A microcanonical entropy correcting finite-size effects in small systems
No full textIn a recent paper (Franzosi (2018 Physica A 494 302)), we have suggested to use the surface entropy, namely the logarithm of the area of a hypersurface of constant energy in the phase space, as an expression for the thermodynamic microcanonical entropy, in place of the standard definition usually known as Boltzmann entropy. In the present manuscript, we have tested the surface entropy on the Fermi-Pasta-Ulam model for which we have computed the caloric equations that derive from both the Boltzmann entropy and the surface entropy. The results achieved clearly show that in the case of the Boltzmann entropy there is a strong dependence of the caloric equation from the system size, whereas in the case of the surface entropy there is no such dependence. We infer that the issues that one encounters when the Boltzmann entropy is used in the statistical description of small systems could be a clue to a deeper defect of this entropy that derives from its basic definition. Furthermore, we show that the surface entropy is well founded from a mathematical point of view, and we show that it is the only admissible entropy definition, for an isolated and finite system with a given energy, which is consistent with the postulate of equal a priori probability
Topology and classical geometry in (2+1) gravity
No full textThe structure of the spacetime geometry in (2 + 1) gravity is described
by means of a foliation in which the space-like surfaces admit a
tessellation made of polygons. The dynamics of the system is determined
by a set of 't Hooft's rules which specify the time evolution of the
tessellation. We illustrate how the non-trivial topology of the universe
can be described by means of 't Hooft's formalism. The classical
geometry of a universe with the spatial topology of a torus is
considered and the relation between 't Hooft's transitions and modular
transformations is discussed. The universal covering of spacetime is
constructed. The non-trivial topology of an expanding universe gives
origin to a redshift effect; we compute the value of the corresponding
'Hubble's constant'. Simple examples of tessellations for universes with
the spatial topology of a surface with higher genus are presented
Particle decays and space-time kinematics in (2+1) gravity
No full textWe consider the properties of the space-time geometry in the presence of
gravitating spinless particles in (2+1) dimensions. By using 't Hooft
representation of three-dimensional space-time, we give a description of
the decays of gravitating particles and derive the associated kinematic
relations, The effects of gravity on the structure of the
energy-momentum conservation law are discussed. We show that, for a set
of spinless particles, the time evolution of the momenta can be
described by means of a generalized space-time kinematics based on a
particular representation of the braid group
Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals
Full text linkWe consider a generic classical many particle system described by an autonomous Hamiltonian H(x1,...,xN+2) which, in addition, has a conserved quantity V(x1,...,xN+2)=v, so that the Poisson bracket {H,V} vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over sub-manifolds given by the intersection of the constant energy hyper-surfaces with those defined by V(x1,...,xN+2)=v. We show that temperature and higher order derivatives of entropy are microcanonical observable that, under the hypothesis of ergodicity, can be calculated as time averages of suitable functions. We derive the explicit expression of the function that gives the temperature. © 2011 Springer Science+Business Media, LLC
Microcanonical entropy for classical systems
Full text linkThe entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that this entropy definition fixes the problem inherent the exact extensivity of the caloric equation. Furthermore, this entropy reproduces results which are in agreement with the ones predicted with standard Boltzmann entropy when applied to macroscopic systems. On the contrary, the predictions obtained with the standard Boltzmann entropy and with the entropy we propose, are different for small system sizes. Thus, we conclude that the Boltzmann entropy provides a correct description for macroscopic systems whereas extremely small systems should be better described with the entropy that we propose here. © 2017 Elsevier B.V
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