scholarly journals Hořava-Lifshitz Scalar Field Cosmology: Classical and Quantum Viewpoints

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fatimah Tavakoli ◽  
Babak Vakili ◽  
Hossein Ardehali
Keyword(s):  
Scalar Field ◽  
Quantum Cosmology ◽  
Detailed Balance ◽  
Quantum Effects ◽  
Wave Functions ◽  
Classical Solutions ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Quantum Wave ◽  
Scalar Field Cosmology

In this paper, we study a projectable Hořava-Lifshitz cosmology without the detailed balance condition minimally coupled to a nonlinear self-coupling scalar field. In the minisuperspace framework, the super-Hamiltonian of the presented model is constructed by means of which some classical solutions for the scale factor and scalar field are obtained. Since these solutions exhibit various types of singularities, we came up with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology. The resulting quantum wave functions are then used to investigate the possibility of the avoidance of classical singularities due to quantum effects which show themselves important near these singularities.

scholarly journals Revisit on the thermodynamic stability of Hořava–Lifshitz black hole

2018 ◽  
Vol 27 (04) ◽  
pp. 1850048
Author(s):  
Xudong Meng ◽  
Ruihong Wang
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Stability ◽  
Detailed Balance ◽  
De Sitter ◽  
Thermodynamic Variable ◽  
Detailed Balance Condition ◽  
First Law Of Thermodynamics ◽  
Balance Condition ◽  
Lifshitz Black Hole

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter [Formula: see text] in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter [Formula: see text] as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

Convergence of Markov chains in the relative supremum norm

2000 ◽  
Vol 37 (4) ◽  
pp. 1074-1083 ◽  
Author(s):  
Lars Holden
Keyword(s):  
Markov Chain ◽  
Detailed Balance ◽  
Continuity Condition ◽  
Supremum Norm ◽  
Weak Continuity ◽  
Norm Convergence ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Qualitative Understanding ◽  
Doeblin Condition

It is proved that the strong Doeblin condition (i.e., ps(x,y) ≥ asπ(y) for all x,y in the state space) implies convergence in the relative supremum norm for a general Markov chain. The convergence is geometric with rate (1 - as)1/s. If the detailed balance condition and a weak continuity condition are satisfied, then the strong Doeblin condition is equivalent to convergence in the relative supremum norm. Convergence in other norms under weaker assumptions is proved. The results give qualitative understanding of the convergence.

Convergence to the equilibrium for the Pauli equation without detailed balance condition

2005 ◽  
Vol 341 (1) ◽  
pp. 5-10 ◽  
Author(s):  
Naoufel Ben Abdallah ◽  
Miguel Escobedo ◽  
Stéphane Mischler
Keyword(s):  
Detailed Balance ◽  
Pauli Equation ◽  
Detailed Balance Condition ◽  
Balance Condition

Some non-equilibrium invariant states for the asymmetric exclusion QMS at level one

2015 ◽  
Vol 18 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Julio C. García ◽  
Fernando Guerrero-Poblete
Keyword(s):  
Detailed Balance ◽  
Necessary Condition ◽  
Invariant State ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Starting Point ◽  
Invariant States ◽  
Asymmetric Exclusion ◽  
The One ◽  
Non Equilibrium

We review the Asymmetric Exclusion QMS in the light of new results, taking as a starting point the dynamics in the one particle space. We give a condition for the Asymmetric Exclusion QMS to be conservative, prove that an invariant state is necessarily diagonal and give conditions on eigenvalues of such an invariant state. We also give, a necessary condition to annul the generator of the predual semigroup; with this and the weighted detailed balance condition, we propose a method to construct some non-equilibrium invariant states.

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