223,204 research outputs found
The ideal energy of classical lattice dynamics
We define, as local quantities, the least energy and momentum allowed by
quantum mechanics and special relativity for physical realizations of some
classical lattice dynamics. These definitions depend on local rates of
finite-state change. In two example dynamics, we see that these rates evolve
like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335
On the relation between the second law of thermodynamics and classical and quantum mechanics
In textbooks on statistical mechanics, one finds often arguments based on
classical mechanics, phase space and ergodicity in order to justify the second
law of thermodynamics. However, the basic equations of motion of classical
mechanics are deterministic and reversible, while the second law of
thermodynamics is irreversible and not deterministic, because it states that a
system forgets its past when approaching equilibrium. I argue that all
"derivations" of the second law of thermodynamics from classical mechanics
include additional assumptions that are not part of classical mechanics. The
same holds for Boltzmann's H-theorem. Furthermore, I argue that the
coarse-graining of phase-space that is used when deriving the second law cannot
be viewed as an expression of our ignorance of the details of the microscopic
state of the system, but reflects the fact that the state of a system is fully
specified by using only a finite number of bits, as implied by the concept of
entropy, which is related to the number of different microstates that a closed
system can have. While quantum mechanics, as described by the Schroedinger
equation, puts this latter statement on a firm ground, it cannot explain the
irreversibility and stochasticity inherent in the second law.Comment: Invited talk given on the 2012 "March meeting" of the German Physical
Society To appear in: B. Falkenburg and M. Morrison (eds.), Why more is
different (Springer Verlag, 2014
On classical finite probability theory as a quantum probability calculus
This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The point is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting
Wave Packet Spreading: Temperature and Squeezing Effects with Applications to Quantum Measurement and Decoherence
A localized free particle is represented by a wave packet and its motion is
discussed in most quantum mechanics textbooks. Implicit in these discussions is
the assumption of zero temperature. We discuss how the effects of finite
temperature and squeezing can be incorporated in an elementary manner. The
results show how the introduction of simple tools and ideas can bring the
reader into contact with topics at the frontiers of research in quantum
mechanics. We discuss the standard quantum limit, which is of interest in the
measurement of small forces, and decoherence of a mixed (``Schrodinger cat'')
state, which has implications for current research in quantum computation,
entanglement, and the quantum-classical interface
A Quantum Approach to Classical Statistical Mechanics
We present a new approach to study the thermodynamic properties of
-dimensional classical systems by reducing the problem to the computation of
ground state properties of a -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 adiabatic 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 and , for the temperature and magnetic field, respectively. Other
annealing strategies, as well as their potential speed-up, are also discussed.Comment: 4 pages, no figure
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