Related papers: Alternative Hamiltonian Desciptions and Statistica…
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…
Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
For the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D, two different Hamiltonian are given describing the same classical dynamics; however, their quantum dynamics behavior are different.
We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more…
Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…