Rare Earth Ions in Random Crystal Fields (original) (raw)

J. Phys. A: Math. Theor. 45 115206 (2012)

Journal of Physics A Mathematical and Theoretical

In two recent papers we have shown how one-particle and few-particle lattice Green's functions can be calculated efficiently for models with only nearestneighbor hopping, using continued fractions. Here, we show that a similar type of solution is possible for models with longer (but finite) range hopping.

1eTTEL 2008-2-2 Europhysics Letters PREPRINT

2004

PACS. 71.10.Pm – Fermions in reduced dimensions. PACS. 71.27.+a – Strongly correlated electron systems. Abstract. – The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion U. To achieve this goal we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angleresolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ. The finite-energy spectral dispersions recently observed in quasi-one-dimensional (1D) metals by angle-resolved photoelectron spectroscopy (ARPES) reveal significant discrepancies from the conventional band-structure description [1,2]. The study of the microscopic mechanisms behind these unusual finite-energy spectral properties remains until now an in...

arXiv:physics/0601009v3 [physics.ed-ph] 14 Oct 2013

In this manuscript various components of research are listed and briefly discussed. The topics considered in this write-up cover a part of the research methodology paper of Master of Philosophy (M.Phil.) course and Doctor of Philosophy (Ph.D.) course. The manuscript is intended for students and research scholars of science subjects such as mathematics, physics, chemistry, statistics, biology and computer science. Various stages of research are discussed in detail. Special care has been taken to motivate the young researchers to take up challenging problems. Ten assignment works are given. For the benefit of young researchers a short interview with three eminent scientists is included at the end of the manuscript. * Electronic address: rajasekar@cnld.bdu.ac.in

Reports on Mathematical Physics 64 (3), 367-393

In this note we investigate in detail the spectrum of the Schroedinger Hamiltonian with a configuration of three equally spaced one-dimensional point interactions (Dirac distributions), with the external ones having the same negative coupling constant. It will be seen that despite its simplicity, such a toy model exhibits a fairly rich variety of spectral combinations as the two coupling constants and the separation distance are manipulated. By analysing the equation determining the square root of the absolute value of the ground state energy and those determining the same quantity for the two possible excited states, we explicitly calculate the eigenvalues for all possible values of the separation distance and the two coupling constants. As a result of our analysis, we provide the conditions in terms of the three parameters in order to have the emergence of such excited states. Furthermore, we use our findings in order to get the confirmation of the fact that the Hamiltonian with such a configuration of three simple point interactions whose coupling constants undergo a special scaling in terms of the vanishing separation distance, converges in the norm resolvent sense to the Hamiltonian with an attractive δ -interaction centred at the origin, as was shown by Exner and collaborators making the result previously obtained by Cheon et al. mathematically rigorous.

Integral Representation of the Random-Phase Approximation Correlation Energy

Physical Review Letters

Using the spectral function F'(z)/F(z) the RPA correlation energy and other properties of a finite system can be written as a contour integral in a compact way. This yields a transparent expression and reduces drastically the numerical efforts for obtaining reliable values. The method applied to pairing vibrations in rotating nuclei as an illustrative example. PACS numbers: 21.60.Jz, 36.40.Gk Various problems considered in many-body physics of finite quantum systems can be treated in terms of a Hamiltonian which is quadratic in the creation and annihilation operators (see for example [1]). The mean field approximation (MF) and the random phase approximation (RPA) are the well known examples where the dynamics of complicated system is reducing to dynamics described by a quadratic Hamiltonian. These approximations have been proven to be quite successful in many applications to mesoscopic systems like nuclei [2-4] and metallic clusters [5].

Comment on “Optimization of Ground- and Excited-State Wave Functions and van der Waals Clusters”

Physical Review Letters, 2007

A quantum Monte Carlo method is introduced to optimize excited state trial wavefunctions. The method is applied in a correlation function Monte Carlo calculation to compute ground and excited state energies of bosonic van der Waals clusters of upto seven particles. The calculations are performed using trial wavefunctions with general three-body correlations.

PUEC 2018 - Statistical Physics Section

2018

This paper represents the absolute winner Team Sci-Tech's solutions to Physics Unlimited Explorer Competition 2018 and is a good study material for those who want to study statistical physics. In this paper we'll derive and analyze the properties of statistical mechanics in detail. In fact most of the identities we'll derive are already discussed in textbooks but we will reflect our perspective and understanding through solving various examples and exercises. We assume that the reader is familiar with combinatorics and thermodynamics. The subject can be found in the attached link.