scholarly journals Smeared quantum lattices exhibiting 𝒫𝒯-symmetry with positive 𝒫

2012 ◽  
Vol 61 (2-3) ◽  
pp. 111-123 ◽  
Author(s):  
M. Znojil ◽  
H.B. Geyer
Keyword(s):  
Quantum Lattices

Soliton bands in anharmonic quantum lattices

1993 ◽  
Vol 172 (4) ◽  
pp. 229-235 ◽  
Author(s):  
J.C. Eilbeck ◽  
H. Gilhøj ◽  
A.C. Scott
Keyword(s):  
Quantum Lattices

Solitons ofq-deformed quantum lattices and the quantum soliton

2001 ◽  
Vol 34 (48) ◽  
pp. 10463-10474 ◽  
Author(s):  
R K Bullough ◽  
N M Bogoliubov ◽  
A V Rybin ◽  
G G Varzugin ◽  
J Timonen
Keyword(s):  
Quantum Lattices

Bipolar Fuzzy Sets and Equilibrium Relations

2011 ◽  
pp. 129-158
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Clustering ◽  
Theoretical Basis ◽  
Cognitive Map ◽  
Global Regulation ◽  
Quantum Lattices ◽  
Bipolar Fuzzy Sets

Based on bipolar sets and quantum lattices, the concepts of bipolar fuzzy sets and equilibrium relations are presented in this chapter for bipolar fuzzy clustering, coordination, and global regulation. Related theorems are proved. Simulated application examples in multiagent macroeconomics are illustrated. Bipolar fuzzy sets and equilibrium relations provide a theoretical basis for cognitive-map-based bipolar decision, coordination, and global regulation.

scholarly journals Time-Dependent Variational Principle for Quantum Lattices

2011 ◽  
Vol 107 (7) ◽  
Author(s):  
Jutho Haegeman ◽  
J. Ignacio Cirac ◽  
Tobias J. Osborne ◽  
Iztok Pižorn ◽  
Henri Verschelde ◽  
...  
Keyword(s):  
Variational Principle ◽  
Time Dependent ◽  
Quantum Lattices

Bipolar Quantum Lattice and Dynamic Triangular Norms

2011 ◽  
pp. 97-128
Keyword(s):  
Fuzzy Logic ◽  
Quantum Theory ◽  
Partially Ordered Sets ◽  
Dynamic Environments ◽  
Boolean Logic ◽  
Quantum Lattice ◽  
Triangular Norms ◽  
Fuzzy Lattice ◽  
Quantum Lattices ◽  
Complete Quantum

Bipolar quantum lattice (BQL) and dynamic triangular norms (t-norms) are presented in this chapter. BQLs are defined as special types of bipolar partially ordered sets or posets. It is shown that bipolar quantum entanglement is definable on BQLs. With the addition of fuzziness, BDL is extended to a bipolar dynamic fuzzy logic (BDFL). The essential part of BDFL consists of bipolar dynamic triangular norms (t-norms) and their co-norms which extend their truth-based counterparts from a static unipolar fuzzy lattice to a bipolar dynamic quantum lattice. BDFL has the advantage in dealing with uncertainties in bipolar dynamic environments. With bipolar quantum lattices (crisp or fuzzy), the concepts of bipolar symmetry and quasi-symmetry are defined which form a basis toward a logically complete quantum theory. The concepts of strict bipolarity, linearity, and integrity of BQLs are introduced. A recovery theorem is presented for the depolarization of any strict BQL to Boolean logic. The recovery theorem reinforces the computability of BDL or BDFL.

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