Collective motions in nuclei and the spectrum generating algebras T5 × SO(3), GL(3,R), and CM(3)

1976 ◽  
Vol 54 (9) ◽  
pp. 970-996 ◽  
Author(s):  
P. Gulshani ◽  
D. J. Rowe
Keyword(s):  
Discrete System ◽  
Quantum Mechanical ◽  
Body System ◽  
Quantum Mechanical System ◽  
Many Body ◽  
Straightforward Generalization ◽  
Collective Motions ◽  
Collective Hamiltonian ◽  
Full Quantum ◽  
Rotational Mass

Cusson's classical treatment of the collective rotations of a discrete system of N particles is extended to the full quantum mechanical system by means of a straightforward generalization of Villars' canonical transformation. In this manner, Bohr's collective Hamiltonian, with various values for the rotational mass, is microscopically derived. The nature and criteria for the existence of various collective flows in a many-body system are also given. The collective parts of the Hamiltonian are then separately expressed in original particle coordinates and momenta and in this manner the possibility of microscopic calculations for the collective motions is suggested. Finally appropriate microscopic Hamiltonians for the S.G.A.'s T5 × SO(3), GL(3,R), and CM(3) are determined.

scholarly journals The universe from a single particle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Michael Freedman ◽  
Modjtaba Shokrian Zini
Keyword(s):  
Quantum Mechanics ◽  
Single Particle ◽  
Quantum Mechanical ◽  
Local Minima ◽  
Quantum Mechanical System ◽  
Many Body ◽  
Gaussian Unitary Ensemble ◽  
Interacting Systems ◽  
The Universe ◽  
Unitary Ensemble

Abstract We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.

THERMAL PHASES IN FINITE QUANTUM SYSTEMS

2003 ◽  
Vol 17 (28) ◽  
pp. 5093-5100
Author(s):  
D. J. DEAN
Keyword(s):  
Mechanical Systems ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Body System ◽  
Many Body ◽  
Finite Quantum Systems ◽  
Quantum Mechanical Systems ◽  
Increasing Temperature

I will describe the behaviour of two different quantum-mechanical systems as a function of increasing temperature. While these systems are somewhat different, the questions addressed are very similar, namely, how does one describe transitions in phase of a finite many-body system; how does one recognise these transitions in practical calculations; and how may one obtain the order of the transition.

scholarly journals Quantum Gross-Pitaevskii Equation

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Jutho Haegeman ◽  
Damian Draxler ◽  
Vid Stojevic ◽  
Ignacio Cirac ◽  
Tobias Osborne ◽  
...  
Keyword(s):  
Mean Field ◽  
Pitaevskii Equation ◽  
Matrix Product ◽  
Steady State Response ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
State Response ◽  
Quantum Liquids ◽  
Full Quantum

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system —including entanglement and correlations— and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov – de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

scholarly journals The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

2021 ◽  
Author(s):  
Ladislaus Alexander Bányai
Keyword(s):  
Solid State ◽  
Analogous Result ◽  
Charged Particles ◽  
Coulomb Gauge ◽  
Quantum Mechanical ◽  
Photon Propagator ◽  
Coulomb Interactions ◽  
Many Body ◽  
Transverse Current ◽  
Current Interaction

AbstractWe extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

Quantitative Prediction of Aggregation‐Induced Emission: A Full Quantum Mechanical Approach to the Optical Spectra

2020 ◽  
Vol 132 (28) ◽  
pp. 11647-11652
Author(s):  
Wei Zhang ◽  
Jinfeng Liu ◽  
Xinsheng Jin ◽  
Xinggui Gu ◽  
Xiao Cheng Zeng ◽  
...  
Keyword(s):  
Optical Spectra ◽  
Quantitative Prediction ◽  
Quantum Mechanical ◽  
Aggregation Induced Emission ◽  
Mechanical Approach ◽  
Quantum Mechanical Approach ◽  
Full Quantum
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