scholarly journals Quantum graphs and dimensional crossover: the honeycomb

2019 ◽  
Vol 10 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Riccardo Adami ◽  
Simone Dovetta ◽  
Alice Ruighi
Keyword(s):  
Ground States ◽  
Dimensional Crossover ◽  
Quantum Graphs ◽  
Graph Structure ◽  
Two Dimensional ◽  
Grid Graph ◽  
Metric Graphs ◽  
Square Grid ◽  
One Dimensional ◽  
Threshold Phenomena

Abstract We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schrödinger Equation on doubly-periodic metric graphs. We extend the results known for the two–dimensional square grid graph to the honeycomb, made of infinitely-many identical hexagons. Specifically, we show how the coexistence between one–dimensional and two–dimensional scales in the graph structure leads to the emergence of threshold phenomena known as dimensional crossover.

One-Dimensional Looped Chain and Two-Dimensional Square Grid Coordination Polymers: Encapsulation of Bis(1,2,4-Triazole)-trans -cyclohexane into the Voids

2019 ◽  
Vol 2019 (5) ◽  
pp. 543-543
Author(s):  
Nayarassery N. Adarsh ◽  
Marinela M. Dîrtu ◽  
Philippe Guionneau ◽  
Eamonn Devlin ◽  
Yiannis Sanakis ◽  
...  
Keyword(s):  
Coordination Polymers ◽  
Two Dimensional ◽  
Square Grid ◽  
One Dimensional

scholarly journals ORDERING FROM FRUSTRATION IN A STRONGLY CORRELATED ONE-DIMENSIONAL SYSTEM

2009 ◽  
Vol 23 (18) ◽  
pp. 3687-3708
Author(s):  
SIDDHARTHA LAL ◽  
MUKUL S. LAAD
Keyword(s):  
Phase Diagram ◽  
Quantum Critical Point ◽  
Ground States ◽  
Charge Order ◽  
Dimensional System ◽  
Dimensional Crossover ◽  
Coulomb Interactions ◽  
One Dimensional ◽  
Spin Order ◽  
Quantum Critical

We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered (CO) ground states (Wigner and Peierls) as the strength of the longer range interactions is varied. At lower energies, the two CO states drive different spin-ordered ground states (Heisenberg antiferromagnet and dimerised respectively), reminiscent of the phase diagram of the TMTTF and TMTSF organic charge transfer salts. Several response functions computed in the quantum critical regime bear a remarkable resemblance to recent experimental observations related to CO in the organic TMTTF systems. RPA studies of coupled chains reveal a phase diagram with the ordered phase extended to finite temperatures and a phase boundary ending at a quantum critical point (QCP). Critical quantum fluctuations at the QCP enhance the transverse dispersion, leading to a dimensional crossover and a T = 0 deconfinement transition from insulating chains to anisotropic metallic planar behavior. Numerical estimates for the hierarchy of energy scales associated with charge and spin order and the dimensional crossover compare well with the values obtained experimentally. This leads us to propose that the TMTTF and TMTSF systems are proximate to a QCP associated with T = 0 charge order.

scholarly journals Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

Open Physics ◽  
2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Vladimír Tichý ◽  
Lubomír Skála ◽  
René Hudec
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground States ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
One Dimensional

AbstractThis paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

scholarly journals Two-dimensional crossover and strong coupling of plasmon excitations in arrays of one-dimensional atomic wires

2016 ◽  
Vol 93 (16) ◽  
Author(s):  
T. Lichtenstein ◽  
J. Aulbach ◽  
J. Schäfer ◽  
R. Claessen ◽  
C. Tegenkamp ◽  
...  
Keyword(s):  
Strong Coupling ◽  
Dimensional Crossover ◽  
Two Dimensional ◽  
One Dimensional ◽  
Atomic Wires

One-Dimensional Looped Chain and Two-Dimensional Square Grid Coordination Polymers: Encapsulation of Bis(1,2,4-Triazole)-trans -cyclohexane into the Voids

2018 ◽  
Vol 2019 (5) ◽  
pp. 585-591 ◽  
Author(s):  
Nayarassery N. Adarsh ◽  
Marinela M. Dîrtu ◽  
Philippe Guionneau ◽  
Eamonn Devlin ◽  
Yiannis Sanakis ◽  
...  
Keyword(s):  
Coordination Polymers ◽  
Two Dimensional ◽  
Square Grid ◽  
One Dimensional

scholarly journals Threshold phenomena and existence results for NLS ground states on metric graphs

2016 ◽  
Vol 271 (1) ◽  
pp. 201-223 ◽  
Author(s):  
Riccardo Adami ◽  
Enrico Serra ◽  
Paolo Tilli
Keyword(s):  
Ground States ◽  
Existence Results ◽  
Metric Graphs ◽  
Threshold Phenomena

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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