Friction in a Model of Hamiltonian Dynamics

We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle’s trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest.

“A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion.”—— Aristotle     

Hamiltonian for a Relativistic Particle with Linear Dissipation

A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The hamiltonian for a relativistic particle with linear dissipation is obtained. An example of this approach is given. PACS: 45.20.Jj     

二维各向同性谐振子的双波描述

二维各同性谐振子体系除哈密顿量外还有三个独立的守恒量。本文给出了对这些不同描术宾比较。     

Point Source of Nonstationary Polarized Radiation in a Homogeneous Fluctuating Medium

Based on the method of irreducible representations of the rotation group, we obtain an analytical expression for the source function of the radiative transport equation with allowance for polarization of light. The scattering indicatrix is assumed Rayleigh. It is shown that not all polarization characteristics of light in a fluctuating medium are lost in time. Some of them always carry information about the emitter and the scattering medium.     

分区均匀介质静电场的求解

1分区均匀介质静电场求解方法的回顾分区均匀介质静电场的求解是电磁学课程中比较有难度和有特色的内容.有两种情形的分区均匀介质静电场问题可以解析求解:一种是介质-介质界面与撤去电介质时的电场线平行;另一种是介质-介质界面与撤去电介质时的电场线垂直.它是唯一性定理应用的一个生动的实例,并且涉及到静     

Anderson Parabolic Model for a Quasi-Stationary Medium

We study the Anderson Parabolic Model for a random medium which is a product of an i.i.d. space-like random field and a white noise. The model has long range space-time correlations and is intermediate between the stationary case and the “turbulent” one, which were studied in previous works. Under some natural assumptions on the distribution of the space potential, we prove existence and uniqueness, and derive the long time asymptotics for the annealed moments, and the “semi-annealed” ones, for which expectation is taken only w.r.t. the white noise. A conjecture for the fully quenched case is discussed on a simplified model. C. Boldrighini and A. Pellegrinotti are partially supported by INdAM (GNFM) and MURST research founds.     

Field of a Point Source Within Perfectly Conducting Parallel-Plates in a Homogeneous Biisotropic Medium

The spherical wave scattering response by a perfectly conducting open–ended waveguide in a biisotropic medium is obtained. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left–handed or a right–handed Beltrami field. Here, we explicitly consider the scattering of the left–handed field component, that of the other scalar field being analogously tractable. The solution is constructed with the aid of the Wiener–Hopf technique.     

A Simple Model for the Propagation of Rectangular-Pulse Modulated Carrier Through a Single-Mode Homogeneous Waveguide

A simple model for the propagation of rectangular-pulse modulated carrier through a single-mode homogeneous waveguide is derived based on the results obtained through saddle point method and is validated by comparison with the numerical results of Hosono's method. Unlike the previously obtained results, this model is in the form of segmented linear function and easy to use for engineering. This model also provides a simple expression for the minimum pulse width applicable for the frequency measurement based on group time-delay.     

Local Stability of Perfect Alignment for a Spatially Homogeneous Kinetic Model

We prove the nonlinear local stability of Dirac masses for a kinetic model of alignment of particles on the unit sphere, each point of the unit sphere representing a direction. A population concentrated in a Dirac mass then corresponds to the global alignment of all individuals. The main difficulty of this model is the lack of conserved quantities and the absence of an energy that would decrease for any initial condition. We overcome this difficulty thanks to a functional which is decreasing in time in a neighborhood of any Dirac mass (in the sense of the Wasserstein distance). The results are then extended to the case where the unit sphere is replaced by a general Riemannian manifold.     

Properties of Linear Entropy in k-Photon Jaynes-Cummings Model with Stark Shift and Kerr-Like Medium

The time evolution of the linear entropy of an taking into consideration Stark shift and Kerr-like medium. atom in k-photon daynes-Cummings model is investigated The effect of both the Stark shift and Kerr-like medium on the linear entropy is analyzed using a numerical technique for the field initially in coherent state and in even coherent state. The results show that the presence of the Kerr-like medium and Stark shift has an important effect on the properties of the entropy and entanglement. It is also shown that the setting of the initial state plays a significant role in the evolution of the linear entropy and entanglement.     

Quantized Fermi Accelerator: A Soluble Model for Quantum Friction

The motion of a particle constrained to move inside a box with a movable wall is quantized. The semiclassical, adiabatic and exact solutions are worked out. The time-dependent density matrix is found in closed form. The motions of the heavy and the light parts of the system, described by appropriate reduced density matrices, are discussed. General comments about quantum friction are made.     

Effect of a Homogeneous Dielectric Medium on the Luminescence of Singlet Oxygen

Russian Physics Journal - Results of an analysis of our and literature data devoted to the study of the effect of a homogeneous dielectric medium on the rate constant of the $$...     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

An Anisotropic Homogeneous Cosmological Model in a Modified Brans-Dicke Cosmology

Adding the cosmological term, which is assumed to be variable in Brans-Dicke theory we have discussed about a spatially homogeneous and anisotropic cosmological model corresponding to Bianchi type-I solution. The physical and geometrical properties of this model has been discussed. Finally this model has been transformed to the original form (1961) of Brans-Dicke theory (including a variable cosmological term).     

A Light-Cone QCD Inspired Effective Hamiltonian Model for Pseudoscalar and Scalar Mesons

Considering the one-gluon exchange interaction and phenomenological quark confinement potential, an improved light-cone effective Hamiltonian for mesons and the corresponding radial mass eigen equations in angular momentum representation is obtained. Solving the J = 0 eigen equations numerically and using a set of adjustable parameters, the obtained solutions for ground states and radial excited states can simultaneously describe both pseudoscalar and scalar flavour-off-diagonal mesons. Some radial excited states are also predicted and wait for experimental test. More results for the vector and axial vector mesons are expected.     

A Model for Diffuse Breakdown in High Pressure Gases at Homogeneous Electric Field Strengs

A model of the breakdown in high pressure gases is presented taking into consideration the finite voltage rise time at the discharge electrodes and a finite initial charge carrier density in the gap. Several types of breakdown could be distinguished important for several applications. Thus, the range of existence of high pressure laser discharges at a given preionization density and circuit parameters can be calculated. Moreover, the change in the breakdown characteristics of high pressure gases at high temperatures is explained. This behaviour seems to be important for understanding the physical processes in circuit breaker chambers.     

Collective Hamiltonian for Multi-O(4) Model

The collective Hamiltonian up to the fourth order for multi-O(4) model is derived based on the self-consistent collective-coordinate (SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov (TDHB) theory.The validity of the collective Hamiltonian is checked in the two special cases of the multi-O(4) modelthe case where the number of the shells is equal to one (a single j-shell case),and the case where the Hartree-Bogoliubov equilibrium point is spherical (the spherical case).The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.     

Path Integral for an Effective Two Level Atom in a Kerr-Like Medium and Stark Shift with a Pseudo Hermitian Hamiltonian

We use the coherent state path integral and a angular model for the spin to solve the generalized Jaynes-Cummings model with a pseudo-hermitian Hamiltonian and nonlinear Kerr cavity. The propagators are given explicitly as perturbation series. These are summed up exactly. The energy spectrum and the bi-orthonormal basis of states are deduced.     

Approach to Equilibrium in a Microscopic Model of Friction

We consider the time evolution of a disk under the action of a constant force and interacting with a free gas in the mean-field approximation. Letting V₀>0 be the initial velocity of the disk and V_∞>0 its equilibrium velocity, namely the one for which the external field is balanced by the friction force exerted by the background, we show that, if V_∞−V₀ is positive and sufficiently small, then the disk reaches V_∞ with the power law t^−(d+2), d=1,2,3 being the dimension of the physical space. The reason for this behavior is the long tail memory due to recollisions. Any Markovian approximation (or simply neglecting the recollisions) yields an exponential approach to equilibrium.     

Model Hamiltonian for the Quantum Anomalous Hall State in Iron-Halogenide

We examine quantum anomalous Hall(QAH) insulators with intrinsic magnetism displaying quantized Hall conductance at zero magnetic fields.The spin-momentum locking of the topological edge stats promises QAH insulators with great potential in device applications in the field of spintronics.Here,we generalize Haldane’s model on the honeycomb lattice to a more realistic two-orbital case without the artificial real-space complex hopping.Instead,we introduce an intraorbital coupling,stemming directly ...