PT quantum mechanics - Recent results

2012 ◽  
Author(s):  
Carl M. Bender
Keyword(s):  
Quantum Mechanics ◽  
Pt Quantum Mechanics

scholarly journals Vector Models in $\mathcal{PT}$ Quantum Mechanics

2013 ◽  
Vol 52 (7) ◽  
pp. 2187-2195 ◽  
Author(s):  
Katherine Jones-Smith ◽  
Rudolph Kalveks
Keyword(s):  
Quantum Mechanics ◽  
Pt Quantum Mechanics

scholarly journals Compatibility for probabilistic theories

2016 ◽  
Vol 66 (2) ◽  
Author(s):  
Stan Gudder
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Quantum Logic ◽  
Probabilistic Theory ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Positive Vector ◽  
Vector Valued ◽  
Pt Quantum Mechanics ◽  
Probabilistic Theories

AbstractWe define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT. We consider a PT called a concrete quantum logic that may have compatibility index strictly between 0 and 1, but we have not been able to show this yet. Finally, we show that observables in a PT can be represented by positive, vector-valued measures.

scholarly journals Gibbs States, Algebraic Dynamics and Generalized Riesz Systems

2020 ◽  
Vol 14 (8) ◽  
Author(s):  
F. Bagarello ◽  
H. Inoue ◽  
C. Trapani
Keyword(s):  
Quantum Mechanics ◽  
Time Evolution ◽  
Physical System ◽  
Orthonormal Basis ◽  
Gibbs States ◽  
Real Spectrum ◽  
Algebraic Dynamics ◽  
The Times ◽  
Pt Quantum Mechanics

AbstractIn PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita–Takesaki theory in our context.

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