scholarly journals Quantum Lattice Boltzmann Study of Random-Mass Dirac Fermions in One Dimension

2018 ◽  
pp. 321-330
Author(s):  
Ch. B. Mendl ◽  
S. Palpacelli ◽  
A. Kamenev ◽  
S. Succi
Keyword(s):  
Lattice Boltzmann ◽  
One Dimension ◽  
Dirac Fermions ◽  
Quantum Lattice ◽  
Random Mass

Isotropy of three-dimensional quantum lattice Boltzmann schemes

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
P. J. Dellar ◽  
D. Lapitski ◽  
S. Palpacelli ◽  
S. Succi
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Quantum Lattice

scholarly journals Renormalization group analysis of Dirac fermions with a random mass

2021 ◽  
Vol 104 (17) ◽  
Author(s):  
Zhiming Pan ◽  
Tong Wang ◽  
Tomi Ohtsuki ◽  
Ryuichi Shindou
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Dirac Fermions ◽  
Renormalization Group Analysis ◽  
Random Mass

ONE-DIMENSIONAL QUANTUM LATTICE BOLTZMANN SCHEME FOR THE NONLINEAR DIRAC EQUATION

2013 ◽  
Vol 24 (12) ◽  
pp. 1340001 ◽  
Author(s):  
SILVIA PALPACELLI ◽  
PAUL ROMATSCHKE ◽  
SAURO SUCCI
Keyword(s):  
Dirac Equation ◽  
Lattice Boltzmann ◽  
Spontaneous Breaking ◽  
Mass Generation ◽  
Quantum Lattice ◽  
One Dimensional ◽  
Dynamic Mass ◽  
Nonlinear Dirac Equation ◽  
Njl Model ◽  
Lattice Boltzmann Scheme

We develop a quantum lattice Boltzmann (QLB) scheme for the Dirac equation with a nonlinear fermion interaction provided by the Nambu–Jona-Lasinio (NJL) model. Numerical simulations in 1 + 1 space-time dimensions, provide evidence of dynamic mass generation, through spontaneous breaking of chiral symmetry.

scholarly journals Quantum lattice Boltzmann is a quantum walk

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Sauro Succi ◽  
François Fillion-Gourdeau ◽  
Silvia Palpacelli
Keyword(s):  
Lattice Boltzmann ◽  
Quantum Walk ◽  
Quantum Lattice

Quantum Lattice Boltzmann (QLB)

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Lattice Boltzmann ◽  
Quantum Physics ◽  
Newtonian Mechanics ◽  
Quantum Lattice ◽  
Recent Developments

The Lattice Boltzmann concepts and applications described so far refer to classical, i.e., non-quantum physics. However, the LB formalism is not restricted to classical Newtonian mechanics and indeed an LB formulation of quantum mechanics, going by the name of quantum LB (QLB) has been in existence for more than two decades. Even though it would far-fetched to say that QLB represents a mainstream, in the recent years it has captured some revived interest, mostly on account of recent developments in quantum-computing research. This chapter provides an account of the QLB formulation: stay tuned, LBE goes quantum!

Numerical comparison of 1D quantum lattice Boltzmann models

2009 ◽  
Vol 2009 (06) ◽  
pp. P06004 ◽  
Author(s):  
Miguel Alfonso Valdivieso Colmenares ◽  
José Daniel Muñoz Castaño
Keyword(s):  
Lattice Boltzmann ◽  
Numerical Comparison ◽  
Quantum Lattice ◽  
Lattice Boltzmann Models

scholarly journals Convergence of a three-dimensional quantum lattice Boltzmann scheme towards solutions of the Dirac equation

2011 ◽  
Vol 369 (1944) ◽  
pp. 2155-2163 ◽  
Author(s):  
Denis Lapitski ◽  
Paul J. Dellar
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Lattice Boltzmann ◽  
Schrodinger Equation ◽  
Fourier Transforms ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Relativistic Limit ◽  
Quantum Lattice ◽  
Lattice Boltzmann Scheme

We investigate the convergence properties of a three-dimensional quantum lattice Boltzmann scheme for the Dirac equation. These schemes were constructed as discretizations of the Dirac equation based on operator splitting to separate the streaming along the three coordinate axes, but their output has previously only been compared against solutions of the Schrödinger equation. The Schrödinger equation arises as the non-relativistic limit of the Dirac equation, describing solutions that vary slowly compared with the Compton frequency. We demonstrate first-order convergence towards solutions of the Dirac equation obtained by an independent numerical method based on fast Fourier transforms and matrix exponentiation.

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