10/27 Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics

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Time: 1:45pm~3:10pm, October 27 (Thursday)
Title: Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics

Speaker: Doc. Dr Petr Jizba
(Department of Physics, Czech Technical University in Prague)
Place: online speech https://meet.google.com/ndj-aqqz-xuo   
            Students should attend the lecture in Science Building III 1F SC157

Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics
P.Jizba
 
The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (eg, Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In my talk I will discuss possible observational effects of GUP systems in their decoherence domain. I first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis’ probability amplitudes, whose non-extensivity parameter q monotonically increases with the GUP deformation parameter β . Secondly, for β < 0 (ie, q < 1      ), I show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, I invoke the Maximal Entropy principle known from estimation theory to reveal connection between the quasi -classical (decoherence) limit of GUP-related quantum theory and non-extensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, the aforementioned quasi-classical regime has relevant observational consequences. I will discuss some of the implications.
 
P. Jizba and J. Korbel, Phys. Rev. Lett. 122 , 120601 (2019).    
P. Jizba, Y. Ma, A. Hayes, and JA Dunningham Phys. Rev. E 93 , 060104(R) (2016)   
P.Jizba,  G. Lambiase, G. Luciano and L. Petruziello, Phys. Rev. D 105, L121501 (2022)
EP Verlinde, JHEP 04 , 029 (2011) 
PD Mannheim and JG O’Brien, Phys. Rev. Lett. 106 , 121101 (2011)