scholarly journals Quantum cosmology of a Hořava–Lifshitz model coupled to radiation

2019 ◽  
Vol 28 (10) ◽  
pp. 1950130
Author(s):  
G. Oliveira-Neto ◽  
L. G. Martins ◽  
G. A. Monerat ◽  
E. V. Corrêa Silva
Keyword(s):  
Detailed Balance ◽  
Gravitational Theory ◽  
Expected Value ◽  
Scale Factor ◽  
Many Worlds ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Variational Formalism ◽  
The Many ◽  
Parameter Values

In the present paper, we canonically quantize a homogeneous and isotropic Hořava–Lifshitz cosmological model, with constant positive spatial sections and coupled to radiation. We consider the projectable version of that gravitational theory without the detailed balance condition. We use the Arnowitt–Deser–Misner (ADM) formalism to write the gravitational Hamiltonian of the model and the Schutz variational formalism to write the perfect fluid Hamiltonian. We find the Wheeler–DeWitt equation for the model, which depends on several parameters. We study the case in which parameter values are chosen so that the solutions to the Wheeler–DeWitt equation are bounded. Initially, we solve it using the Many Worlds interpretation. Using wave packets computed with the solutions to the Wheeler–DeWitt equation, we obtain the scalar factor expected value [Formula: see text]. We show that this quantity oscillates between finite maximum and minimum values and never vanishes. Such result indicates that the model is free from singularities at the quantum level. We reinforce this indication by showing that by subtracting one standard deviation unit from the expected value [Formula: see text], the latter remains positive. Then, we use the DeBroglie–Bohm interpretation. Initially, we compute the Bohm’s trajectories for the scale factor and show that they never vanish. Then, we show that each trajectory agrees with the corresponding [Formula: see text]. Finally, we compute the quantum potential, which helps understanding why the scale factor never vanishes.

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.

Entropy, fluctuation and transport in lattice gas systems with generalized semi-detailed balance

1997 ◽  
Vol 57 (1) ◽  
pp. 175-185 ◽  
Author(s):  
HUDONG CHEN
Keyword(s):  
Lattice Gas ◽  
Detailed Balance ◽  
Statistical Properties ◽  
Continuous Systems ◽  
Physical Processes ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Dirac Type ◽  
Reciprocity Relations ◽  
Non Equilibrium

We describe the existence of an entropy for lattice gas systems of Fermi–Dirac type based on a generalized semi-detailed balance condition. We demonstrate some essential equilibrium and non-equilibrium fluctuation and dissipation properties, including the so-called Onsager's reciprocity relations, as a consequence of this condition. Requirements for the existence of certain statistical properties in discrete lattice gas systems are not directly inferred from those in real continuous systems, but are closely related. Hence understanding in detail the causes and results for lattice gas systems may provide further insights into fundamental microscopic physical processes.

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