Numerical analysis of orthogonal functional systems for finite Fresnel transform

Optical Review - The fundamental formula in an optical system is Rayleigh diffraction integral. In practice, we deal with Fresnel diffraction integral as approximate diffraction formula. Fresnel...     

压力环境下重费米子体系的物性探索

@@@@重费米子体系是近藤晶格中的强关联电子系统,它由于电、磁等相互作用的竞争呈现出丰富的电子基态,而且由于各种相互作用的能量尺度较小,它会对外界参量(压力、掺杂、磁场)的调控比较敏感。文章论述了重费米子体系的基本性质和它在压力环境下的物性演变以及相关的量子临界现象。超导态一般会出现在量子临界点附近,文章特别以“115”超导体系为例,讲述了超导态与其他长程序共存时可能出现的纹络化结构,介绍了如何运用压力下的谱学测量(如转角比热、软点接触隧道谱)来研究压力下重费米子体系的物性特别是超导序参量的对称性。     

压力环境下重费米子体系的物性探索

重费米子体系是近藤晶格中的强关联电子系统,它由于电、磁等相互作用的竞争呈现出丰富的电子基态,而且由于各种相互作用的能量尺度较小,它会对外界参量(压力、掺杂、磁场)的调控比较敏感。文章论述了重费米子体系的基本性质和它在压力环境下的物性演变以及相关的量子临界现象。超导态一般会出现在量子临界点附近,文章特别以“115”超导体系为例,讲述了超导态与其他长程序共存时可能出现的纹络化结构,介绍了如何运用压力下的谱学测量(如转角比热、软点接触隧道谱)来研究压力下重费米子体系的物性特别是超导序参量的对称性。     

Translationally-invariant coupled-cluster method for finite systems

The translational invariant formulation of the coupled-cluster method is presented here at the complete SUB(2) level for a system of nucleons treated as bosons. The correlation amplitudes are solution of a non-linear coupled system of equations. These equations have been solved for light and medium systems, considering the central but still semi-realistic nucleon-nucleon S3 interaction.     

Passive states for finite classical systems

Starting from a passivity condition based on the second law of thermodynamics [12], we show that ground states and Gibbs states (0<<) are essentially the only passive states.Research supported by M. Skodowska-Curie Fund Grant No. OIP74-01416.     

Velocity correlation functions for finite one-dimensional systems

Certain systems consisting of a one-dimensional gas of a finite number of point particles interacting with a “hard-core” potential are considered.We use the technique developed by Jepsen to calculate exactly the velocity correlation functions for these systems. We discover that after a slow decay for times of the order of the relaxation time, there is a “fast” decay to the equilibrium value on a macroscopic time scale characterized by L/v_TH (L is the length of the container and v_TH the thermal velocity).The dependence of the velocity correlation functions on the initial position of the specified particle is also considered. In particular, the behaviour approaching the boundary of the container is analyzed. These considerations are generalized to systems of higher spatial dimension.     

A functional method for condensed systems

Schwingers functional method is applied to the Green functions of the many body problem. By including the “anomalous” Green functions introduced by Gorkov, a formalism results which permits in a natural way the treatment of systems showing “superfluid” properties (“condensed” systems).     

Adiabatic theorem for finite dimensional quantum mechanical systems

A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. An explicitly integrable two-level system is considered as an example. It is demonstrated that the error estimate given by the adiabatic theorem cannot be improved.     

Real-space renormalization-group transformation for finite thickness ising systems

The real-space renormalization group transformation based on the cumulant expansion is modified for systems with free-surface boundary conditions. Free energies and heat capacities of ferromagnetic strips (n x ∞) and slabs (n x ∞ x ∞) are determined over a wide temperature range. The critical or pseudocritical behavior approaches the bulk limit as n → ∞ according to a simple power law, [T_c(n) ? T_c (∞)] ∞n^?λ it is verified that the shift exponent λ is equal to the reciprocal of the critical length exponent.     

A finite slow-motion approximation method for self-gravitating systems

We present a finite approximation procedure for weakly self-gravitating quasi-stationary systems applied to a Lorentz-invariant, non-linear scalar model theory of gravity. We derive lowest order radiation-reaction terms in the equations of motion and compare them with those terms derived using the usual slow-motion method.     

Expectations and entropy inequalities for finite quantum systems

We prove that the relative entropy is decreasing under a trace-preserving expectation inB(K ¹), and we show the connection between this theorem and the strong subadditivity of the entropy. It is also proved that a linear, positive, trace-preserving map ofB(K) into itself such that 1 decreases the value of any convex trace function.     

Time evolution for quantum systems at finite temperature

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check self-consistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable.     

Colour superconductivity in finite systems

We have studied the effects of finite size on the two flavor colour superconducting state. Since the baryon number in the BCS state is only fixed on average, we have projected the state onto a fixed baryon number. The resulting state has been then projected onto a colour-singlet state, by integrating onto the colour group manifold. The effects of both projections have been evaluated numerically.