Quantum mechanics I–few body systems

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Ground State ◽  
Momentum Space ◽  
Quantum Monte Carlo ◽  
Path Integrals ◽  
Scattering Problem ◽  
Quantum Systems ◽  
Matrix Formalism ◽  
Matrix Elements ◽  
State Matrix ◽  
Coupled Channel

Several techniques for obtaining the eigenspectrum and scattering properties of one- and two-body quantum systems are presented. More unusual topics, such as solving the Schrödinger equation in momentum space or implementing relativistic kinematics, are also addressed. A novel quantum Monte Carlo technique that leverages the similarity between path integrals and random walks is developed. An exploration of the method for simple problems is followed by a survey of methods to obtain ground state matrix elements. A review of scattering theory follows. The momentum space T-matrix formalism for scattering is introduced and an efficient numerical method for solving the relevant equations is presented. Finally, the method is extended to the coupled channel scattering problem.

scholarly journals Quantum collisional thermostats

2022 ◽  
Author(s):  
Jorge Tabanera ◽  
Inés Luque ◽  
Samuel L. Jacob ◽  
Massimiliano Esposito ◽  
Felipe Barra ◽  
...  
Keyword(s):  
Open Quantum Systems ◽  
Formal Solution ◽  
Scattering Problem ◽  
Approximate Solutions ◽  
Quantum Systems ◽  
Matrix Formalism ◽  
External Agent ◽  
Far From Equilibrium ◽  
Transfer Matrix Formalism ◽  
Scattering Map

Abstract Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir. Generically, in this operation the external agent performs work onto the system, preventing thermalization when the reservoir is at equilibrium. One can recover thermalization by considering an autonomous global setup where the reservoir particles colliding with the system possess a kinetic degree of freedom. The drawback is that the corresponding scattering problem is rather involved. Here, we present a formal solution of the problem in one dimension and for flat interaction potentials. The solution is based on the transfer matrix formalism and allows one to explore the symmetries of the resulting scattering map. One of these symmetries is micro-reversibility, which is a condition for thermalization. We then introduce two approximations of the scattering map that preserve these symmetries and, consequently, thermalize the system. These relatively simple approximate solutions constitute models of quantum thermostats and are useful tools to study quantum systems in contact with thermal baths. We illustrate their accuracy in a specific example, showing that both are good approximations of the exact scattering problem even in situations far from equilibrium. Moreover, one of the models consists of the removal of certain coherences plus a very specific randomization of the interaction time. These two features allow one to identify as heat the energy transfer due to switching on and off the interaction. Our results prompt the fundamental question of how to distinguish between heat and work from the statistical properties of the exchange of energy between a system and its surroundings.

Quantum spin systems

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Ground State ◽  
Quantum Monte Carlo ◽  
Spin Chain ◽  
Energy Levels ◽  
Discrete Systems ◽  
Quantum Spin ◽  
Lanczos Algorithm ◽  
Quantum Spin Systems ◽  
State Matrix ◽  
Heisenberg Spin Chain

The quantum mechanical underpinnings of magnetism are explored via the Heisenberg model of antiferromagnetism. The Lanczos algorithm is developed and applied to obtain ground state properties of the anisotropic antiferromagnetic Heisenberg spin chain. In particular, the phase diagram for the system magnetization is determined. A quantum Monte Carlo method that is appropriate for discrete systems is also presented. The method leverages the similarity between the Schrödinger equation and the diffusion equation to compute energy levels. The formalism necessary to compute ground state matrix elements is also developed. Finally, the method is tested with an application to the spin chain.

Multiple Coulomb and Nuclear Excitation of 238U with Very Heavy Ions

1977 ◽  
Vol 32 (12) ◽  
pp. 1465-1476 ◽  
Author(s):  
Volker Oberacker ◽  
Gerhard Soff
Keyword(s):  
Ground State ◽  
Heavy Ions ◽  
Energy Levels ◽  
Matrix Elements ◽  
Spin Dependence ◽  
Nuclear Excitation ◽  
Vibration Model ◽  
Analytic Expressions ◽  
Coupled Channel ◽  
The Impact

Abstract Coupled channel calculations for Coulomb and nuclear excitation of the systems 136Xe-238U and 238U-238U have been performed using the rotation-vibration model. The impact parameter-, energy-and spin-dependence of the excitation probabilities are discussed for the ground state-, β-and γ-band up to Jπ = 36+. It is shown that the energy levels and quadrupole matrix elements are strongly influenced by the rotation-vibration interaction. Analytic expressions for the elastic and coupling potentials are presented.

scholarly journals Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2022 ◽  
Vol 130 (1) ◽  
pp. 59
Author(s):  
А.М. Кузьменко ◽  
В.Ю. Иванов ◽  
А.Ю. Тихановский ◽  
А.Г. Пименов ◽  
А.М. Шуваев ◽  
...  
Keyword(s):  
Crystal Field ◽  
Excited States ◽  
Ground State ◽  
Theoretical Study ◽  
Low Frequency ◽  
Local Symmetry ◽  
Matrix Elements ◽  
The Matrix ◽  
Excitation Conditions ◽  
Ground Multiplet

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

scholarly journals The Ghost Anomaly in the 9Be(p, d)8Be Reaction

1976 ◽  
Vol 29 (4) ◽  
pp. 245 ◽  
Author(s):  
FC Barker ◽  
GM Crawley ◽  
PS Miller ◽  
WF Steele
Keyword(s):  
Ground State ◽  
Matrix Formalism ◽  
R Matrix

The ghost of the 8Be ground state has been observed in the 9Be(p, d)8Be reaction, and fitted using a many-level R-matrix formalism.

Theory of Brueckner and Sawada Applied to a Many-Boson Model

1973 ◽  
Vol 51 (3) ◽  
pp. 292-301 ◽  
Author(s):  
M. Razavy ◽  
E. S. Krebes
Keyword(s):  
Ground State ◽  
Transition Point ◽  
Matrix Formalism ◽  
Coupling Constant ◽  
Bogoliubov Approximation ◽  
Wide Range ◽  
Simple Change ◽  
Boson Model ◽  
Repulsive Forces ◽  
Range Of Values

The Bassichis–Foldy model of a simple interacting boson is solved numerically and the results are compared with those obtained by the Bogoliubov approximation and by the Brueckner–Sawada t-matrix formalism. In the normal region, contrary to the widely held view, the Brueckner–Sawada approximation for the energy of the ground state is not reliable for strong, well-behaved, repulsive forces. The Bogoliubov approximation, on the other hand, remains valid for a wide range of values of the coupling constant. In the inverted region, the attractive force causes a population inversion in the levels of the system. For this case a modified Brueckner–Sawada approximation is developed. This method is applied to the calculation of the transition point and the energies of the ground and the first excited states of the system. Here most of the predictions of the modified Brueckner–Sawada approximation are quite accurate. By a simple change in the Bassichis–Foldy model it is shown that even, for two bosons there can be a phase transition. In this model, the derivative of the ground state energy with respect to the coupling constant is discontinuous at the transition point.

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