The Experts below are selected from a list of 216 Experts worldwide ranked by ideXlab platform

S.g. Chung - One of the best experts on this subject based on the ideXlab platform.

Marcello Cini - One of the best experts on this subject based on the ideXlab platform.

  • quantum Mechanics without waves a generalization of Classical Statistical Mechanics
    Annals of Physics, 1999
    Co-Authors: Marcello Cini
    Abstract:

    Abstract We generalize Classical Statistical Mechanics to describe the kynematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the theory). This is possible provided we adopt Feynman's suggestion of dropping the assumption that the probability for an event must always be a positive number. This approach has the advantage of allowing a reformulation of quantum theory in phase space without introducing the unphysical concept of probability amplitudes, together with all the problems concerning their ambiguous properties.

  • measurement in quantum Mechanics and Classical Statistical Mechanics
    Physics Letters A, 1992
    Co-Authors: Marcello Cini, Maurizio Serva
    Abstract:

    Abstract It is shown that the uncertainties (ΔP)2 and (ΔQ)2 in momentum and positiion of a quantum particle can always be expressed as the sum of a Classical term and a quantum term. For quantum states characterized by a product ΔPΔQ〉h it is always possible to reduce the uncertainty in both P and Q by performing measurements of both of them with resolutions ΔP0 and ΔQ0 such that their product is of the order of h. These measurements do not bring into existence values of P and Q which were nonexisting before, as it is usually assumed, but merely restrict the region in phase space allowed for them. This analysis can be used to support the thesis that the old question of the state vector collapse can be solved within the frameworl of the formalism of quantum Mechanics, since it arises from the irreversible character of the increase of knowledge.

Luisberis Velazquez Abad - One of the best experts on this subject based on the ideXlab platform.

  • principles of Classical Statistical Mechanics a perspective from the notion of complementarity
    Annals of Physics, 2012
    Co-Authors: Luisberis Velazquez Abad
    Abstract:

    Abstract Quantum Mechanics and Classical Statistical Mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, Classical Statistical Mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observables I = { I i } , and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of Classical Statistical Mechanics Δ I i Δ η i ≥ k . Here, k is the Boltzmann constant, η i = ∂ S ( I | θ ) / ∂ I i are the restituting generalized forces derived from the entropy S ( I | θ ) of a closed system, which is found in an equilibrium situation driven by certain control parameters θ = { θ α } . These arguments constitute the central ingredients of a reformulation of Classical Statistical Mechanics from the notion of complementarity. In this new framework, Einstein postulate of Classical fluctuation theory d p ( I | θ ) ∼ exp [ S ( I | θ ) / k ] d I appears as the correspondence principle between Classical Statistical Mechanics and thermodynamics in the limit k → 0 , while the existence of uncertainty relations can be associated with the non-commuting character of certain operators.

  • Complementarity in Quantum Mechanics and Classical Statistical Mechanics
    Theoretical Concepts of Quantum Mechanics, 2012
    Co-Authors: Luisberis Velazquez Abad, Sergio Curilef Huichalaf
    Abstract:

    Roughly speaking, complementarity can be understood as the coexistence of multiple properties in the behavior of an object that seem to be contradictory. Although it is possible to switch among different descriptions of these properties, in principle, it is impossible to view them, at the same time, despite their simultaneous coexistence. Therefore, the consideration of all these contradictory properties is absolutely necessary to provide a complete characterization of the object. In physics, complementarity represents a basic principle of quantum theory proposed by Niels Bohr (1; 2), which is closely identified with the Copenhagen interpretation. This notion refers to effects such as the so-called wave-particle duality. In an analogous perspective as the finite character of the speed of light c implies the impossibility of a sharp separation between the notions of space and time, the finite character of the quantum of action h implies the impossibility of a sharp separation between the behavior of a quantum system and its interaction with the measuring instruments. In the early days of quantum Mechanics, Bohr understood that complementarity cannot be a unique feature of quantum theories (3; 4). In fact, he suggested that the thermodynamical quantities of temperature T and energy E should be complementary in the same way as position q and momentum p in quantum Mechanics. According to thermodynamics, the energy E and the temperature T can be simultaneously defined for a thermodynamic system in equilibrium. However, a complete and different viewpoint for the energy-temperature relationship is provided in the framework of Classical Statistical Mechanics (5). Inspired on Gibbs canonical ensemble, Bohr claimed that a definite temperature T can only be attributed to the system if it is submerged into a heat bath1, in which case fluctuations of energy E are unavoidable. Conversely, a definite energy E can only be assigned when the system is put into energetic isolation, thus excluding the simultaneous determination of its temperature T. At first glance, the above reasonings are remarkably analogous to the Bohr’s arguments that support the complementary character between the coordinates q and momentum p. Dimensional analysis suggests the relevance of the following uncertainty relation (6):

Gerardo Ortiz - One of the best experts on this subject based on the ideXlab platform.

  • quantum approach to Classical Statistical Mechanics
    Physical Review Letters, 2007
    Co-Authors: Rolando D Somma, C D Batista, Gerardo Ortiz
    Abstract:

    We present a new approach to study the thermodynamic properties of d-dimensional Classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This Classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing method to simulate Classical systems at finite temperatures. Using the adiabat ic theorem of quantum Mechanics, we derive the rates to assure convergence to the optimal thermodynamic state. For simulated and quantum annealing, we obtain the asymptotic rates of T (t) � (pN)/(kB log t) and (t) � (Nt) ¯ , for the temperature and magnetic field, respectively. Other annealing strategies, as well as their potential speed-up, are also discussed. PACS numbers: 45.10.-b, 05.70.-a, 03.65.Ge An outstanding issue in combinatorial optimization is the classification of problems according to their computationa l complexity. Typically, one defines a cost function that need s to be minimized and the question is how the number of resources (e.g., time) to determine the minimum scales with the problem size N . Long time ago it has been recognized that certain physics problems can be cast in this language. For example, it has been shown that the computation of the ground state energy (or the partition function) of classica l three-dimensional spin glasses belongs to the class of NPcomplete problems [1], i.e. there is no known algorithm that can find the solution with polynomial (in N ) resources. After all, the number of possible microscopic configurations of th e system increases exponentially with the system size N and, unless certain symmetries reduce the complexity, one has to search in an exponentially large state space. This simplific ation happens, for example, in the two-dimensional Ising spin glass [2] (or any planar graph or lattice).

L. De Cesare - One of the best experts on this subject based on the ideXlab platform.