Variational approach to the soft-Coulomb potential in low-dimensional quantum systems

2017 ◽  
Vol 85 (11) ◽  
pp. 834-839 ◽  
Author(s):  
Federico Grasselli
Keyword(s):  
Coulomb Potential ◽  
Variational Approach ◽  
Quantum Systems ◽  
Low Dimensional

scholarly journals Residual Entropy and Critical Behavior of Two Interacting Boson Species in a Double Well

2017 ◽  
Author(s):  
Fabio Lingua ◽  
Andrea Richaud ◽  
Vittorio Penna
Keyword(s):  
Coherent States ◽  
Variational Approach ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Residual Entropy ◽  
Zero Temperature ◽  
Temperature Scenario ◽  
Physical Insight ◽  
Insight Into ◽  
Specific Quantum

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerbly good approximation of the entanglement entropy. Finally, we show that the effectiveness of residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.

Periodic orbits analysis for the Zhou system via variational approach

2019 ◽  
Vol 33 (19) ◽  
pp. 1950212 ◽  
Author(s):  
Chengwei Dong ◽  
Lian Jia
Keyword(s):  
Fixed Points ◽  
Periodic Orbits ◽  
Symbolic Dynamics ◽  
Variational Approach ◽  
Topological Classification ◽  
Dissipative Systems ◽  
Systematic Calculation ◽  
Low Dimensional ◽  
General Method

We proposed a general method for the systematic calculation of unstable cycles in the Zhou system. The variational approach is employed for the cycle search, and we establish interesting symbolic dynamics successfully based on the orbits circuiting property with respect to different fixed points. Upon the defined symbolic rule, cycles with topological length up to five are sought and ordered. Further, upon parameter changes, the homotopy evolution of certain selected cycles are investigated. The topological classification methodology could be widely utilized in other low-dimensional dissipative systems.

scholarly journals Minimizing irreversible losses in quantum systems by local counterdiabatic driving

2017 ◽  
Vol 114 (20) ◽  
pp. E3909-E3916 ◽  
Author(s):  
Dries Sels ◽  
Anatoli Polkovnikov
Keyword(s):  
Variational Approach ◽  
Chaotic Systems ◽  
Chem Phys ◽  
Quantum Systems ◽  
Particle Systems ◽  
Coupling Constant ◽  
Quantum Annealing ◽  
Physical Constraints ◽  
Adiabatic Dynamics

Counterdiabatic driving protocols have been proposed [Demirplak M, Rice SA (2003) J Chem Phys A 107:9937–9945; Berry M (2009) J Phys A Math Theor 42:365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian.

scholarly journals Inelastic Confinement-Induced Resonances in Low-Dimensional Quantum Systems

2012 ◽  
Vol 109 (7) ◽  
Author(s):  
Simon Sala ◽  
Philipp-Immanuel Schneider ◽  
Alejandro Saenz
Keyword(s):  
Quantum Systems ◽  
Low Dimensional

scholarly journals Confinement-Induced Resonances in Low-Dimensional Quantum Systems

2010 ◽  
Vol 104 (15) ◽  
Author(s):  
Elmar Haller ◽  
Manfred J. Mark ◽  
Russell Hart ◽  
Johann G. Danzl ◽  
Lukas Reichsöllner ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Low Dimensional

scholarly journals Divergence of the entanglement range in low-dimensional quantum systems

2006 ◽  
Vol 74 (2) ◽  
Author(s):  
L. Amico ◽  
F. Baroni ◽  
A. Fubini ◽  
D. Patanè ◽  
V. Tognetti ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Low Dimensional
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