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The transport of energy inside protein $\alpha$-helices is studied by deriving a system of quantum equations of motion from the Davydov Hamiltonian with the use of the Schr\"odinger equation and the generalized Ehrenfest theorem. Numerically solving the system of quantum equations of motion for different initial distributions of the amide I energy over the peptide groups confirmed the generation of both moving or stationary Davydov solitons. In this simulation the soliton generation, propagation, and stability were found to be dependent on the symmetry of the exciton-phonon interaction Hamiltonian and the initial site of application of the exciton energy., Comment: 18 pages, 9 figures

We construct an effective commutative Schrodinger equation in Moyal space–time in ( 1 + 1 ) -dimension where both t and x are operator-valued and satisfy t ˆ , x ˆ = i θ . Beginning with a time-reparametrised invariant form of an action we identify the actions of various space–time coordinates and their conjugate momenta on quantum states, represented by Hilbert–Schmidt operators. Since time is also regarded as a configuration space variable, we show how an ‘induced’ inner product can be extracted, so that an appropriate probabilistic interpretation is obtained. We then discuss several other applications of the formalism developed so far.

The radiative response of the classical electron is commonly described by the Lorentz-Abraham-Dirac (LAD) equation. Dirac's derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: "We ... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwanted terms". To substantiate Dirac's approach and clarify the mass renormalization, we introduce the point charge as a limit of extended charges contracting to a point; the fulfillment of conservation laws follows from the relativistic covariant Lagrangian formulation of the problem. We derive the relativistic point charge dynamics described by the LAD equation from the extended charge dynamics in a localization limit by a method which can be viewed as a refinement of Dirac's approach in the spirit of Ehrenfest theorem. The model exhibits the mass renormalization as the cancellation of Coulomb energy with the Poincar\'e cohesive energy. The value of the renormalized mass is not postulated as an arbitrary constant, but is explicitly calculated. The analysis demonstrates that the local energy-momentum conservation laws yield dynamics of a point charge which involves three constants: mass, charge and radiative response coefficient {\theta}. The value of {\theta} depends on the composition of the adjacent potential which generates Poincar\'e forces. The classical value of the radiative response coefficient is singled out by the global requirement that the adjacent potential does not affect the radiated energy balance and affects only the local energy balance involved in the renormalization., Comment: More details are added in the introduction concerning similarities and differences between the original Dirac's approach and our treatment. Several typos are corrected

In this Letter, the nature of phase transition at the critical point of P-V criticality in the extended phase space of RN-AdS black holes has been investigated. By treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume respectively, we introduce the original expressions of Ehrenfest equations directly into the black hole research instead of utilizing the analogy of Ehrenfest equations. We carry out an analytical check of Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the black hole undergoes a second order phase transition at the critical point. This result is consistent with the nature of liquid–gas phase transition at the critical point, hence deepening the understanding of the analogy of charged AdS black holes and liquid–gas systems.

Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase space, directly from classical trajectories. We avoid the need of intermediate steps, like particular solutions to the Schroedinger equation or numerical integration in phase space by considering the system to be initially in a coherent state and by assuming that its early dynamics is governed by the Heller semiclassical approximation. Our result is valid for short propagation times only, but gives non-trivial information on the quantum-classical transition., To appear in Physics Letters A

Ginzburg–Landau theory for studying phase transitions of higher order has been derived using coarse graining and lattice formulation within Ehrenfest thermodynamics. Our developed Hamiltonian leads directly to the functional of the system. We studied the evolution of the order parameter using our developed model equations for third and fourth order phase transitions. The periodic nature of the system can be likened to spatially varying periodic soliton/antisoliton lattice of holes in condensate. This is different from what one observes for any conventional solitary wave in the second order phase regime.

In this paper we briefly discuss the problem of simulating non-adiabatic processes in systems that are usefully modelled using molecular dynamics. In particular we address the problems associated with metals, and describe two methods that can be applied: the Ehrenfest approximation and correlated electron-ion dynamics (CEID). The Ehrenfest approximation is used to successfully describe the friction force experienced by an energetic particle passing through a crystal, but is unable to describe the heating of a wire by an electric current. CEID restores the proper heating. (C) 2008 Elsevier B.V. All rights reserved.

The Kramers’ equation of Brownian motion is applied to investigate the motion of a colloidal particle in a medium subjected to a temperature gradient. The equation is generalized in two ways. First, a chemical force is included in order to account for the non-ideality of the colloidal solution, in the thermodynamic sense. Second, the local disequilibrium of the medium gives rise to a force proportional to the temperature gradient, known as the thermophoretic force in the physics of gases. It is found that the latter force dominates in a rarefied gas, while the chemical force is a good candidate in liquid solutions. The description of the cross-over regime is still unsatisfactory. Next, given the force undergone by a colloidal particle, regardless of its physicochemical origin(s), we determine the velocity response. It is demonstrated that the velocity is not proportional to the applied force, in variance with the Stokes’ law of viscous drag invoked in many works and valid in thermally homogeneous media. An additional effective force tends to drive the particle toward places of higher mobility; that effective force is also proportional to the temperature gradient and can be of the same order of magnitude as the applied force. This conclusion is reached in two different ways, using either a transport equation or statistical-dynamical relations akin to the Ehrenfest theorem in quantum dynamics. Finally, the theoretical formula for the Soret coefficient shows that it is neither proportional to the velocity nor to the force.

Using the generalized Ehrenfest theorem the dynamics of the mean values of a complete set of non-commuting observables (CSNCO) associated to a given Hamiltonian is expressed. We found refined time-dependent invariants of motion (TDIM) for the CSNCO, and associated them with different Lie algebras. We also show that when the CSNCO are related through an antisymmetric matrix, then the characteristic polynomial of the covariance matrix for the CSNCO is also a TDIM. Examples for the Heisemberg, SU(2) and SO(2) groups are outlined.

A simple method for obtaining the expectation values or the ratio of expectation values of different operators composing the transport equation, is presented. This method is based on the Feynmann–Hellmann theorem from quantum mechanics.

The interaction between two harmonic oscillators, a classical and a quantum one, coupled through a linear term, is analyzed by recourse to Ehrenfest's theorem. This model is able to mimic dissipative behaviour for the quantum harmonic oscillator, without violating any quantum rule.

Following Stratonovich, we make a general analysis of the external force manifestations in the dynamics of Markov diffusion processes. The transformation connecting transition densities of the process with the respective (unique) Feynman-Kac kernels induces the local field of accelerations, which equals the gradient of the Feynman-Kac potential and enters the straightforward analog of the Ehrenfest theorem. The latter encompasses not only Nelson's or Zambrini's diffusions but also the familiar non-equilibrium statistical physics processes, like the standard Brownian motion in the external force field (Smoluchowski diffusions).

We derive the information theory form of the quantum statistical operator that reproduces all available (generalized) expectation values and extremalizes the entropy functional proposed by Tsallis. We also demonstrate that a generalized Euler equation relates Tsallis' entropy to the relevant expectation values and to the pertinent Lagrange multipliers. These expectation values are seen to obey the Ehrenfest theorem. Additionally, an appropriate generalization of Jaynes' equation allows one to obtain the Lagrange multipliers from the (input) expectation values.

We point out that the equation of motion derived from the well-known RWA (rotating-wave-approximation) Hamilitonian is inconsistent with the Ehrenfest theorem. By constrast, we find that the very general independent-oscillator model for a dissipative system [Ford et al., Phys. Rev. A 37 (1988) 4419] is consistent with the Ehrenfest theorem.

It is shown that the momentum transfer theorem implies a rough correlation of the diffusion cross section with the slope of the intermolecular potential energy. This is a particular case of the collision Ehrenfest theorem which can be applied in like manner to all of the collision cross sections arising in kinetic theory, thus allowing a qualitative discussion of their dependence on the potential. As an example, relative to the diffusion cross section the viscosity has an increased sensitivity to the curvature of the potential.

Rototranslational motion in simple liquids (like CH 3 CN at 300 K or Ar at 80 K ) is analyzed from the viewpoint of quantum theory. Usually it is assumed that the molecular or atomic motion in the sub-picosecond time range can be treated within classical mechanics, e.g. with the aid of molecular dynamics (MD) simulators. A well known dynamical criterion concerning the applicability of classical mechanics in the present context is discussed. Simple numerical estimations show that the above criterion is violated in the case under consideration. Further analysis based on the quantum mechanical uncertainty relations reveals that the classical-mechanical trajectories cannot be considered to represent physically meaningful concepts in the sub-picosecond time scale. Nevertheless, the success of MD simulations does indicate that some fundamental connection between the quantum and classical treatment of microdynamical processes in liquids may exist. It is argued that in the considered physical context: (i) the “standard” justifications of the applicability of classical mechanics appear to be in contrast to the validity of the uncertainty relations; (ii) the Ehrenfest theorem or Hidden Variables theories cannot support the physical significance of classical trajectories; (iii) Reductionism offers a conceptual basis on which the aforementioned connection can be established.

The effective Ehrenfest hamiltonian for systems where the wavefunction of the quantum part depends parametrically upon “classical” coordinates and momenta is presented and a number of examples are discussed.