scholarly journals Dynamics of Majorana-based qubits operated with an array of tunable gates

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Bela Bauer ◽  
Torsten Karzig ◽  
Ryan Mishmash ◽  
Andrey Antipov ◽  
Jason Alicea
Keyword(s):  
Rabi Oscillation ◽  
Mean Field ◽  
Lattice Models ◽  
Single Wire ◽  
Local Tuning ◽  
Zero Modes ◽  
The Mean ◽  
Majorana Representation ◽  
Majorana Modes ◽  
Qubit Operations

We study the dynamics of Majorana zero modes that are shuttled via local tuning of the electrochemical potential in a superconducting wire. By performing time-dependent simulations of microscopic lattice models, we show that diabatic corrections associated with the moving Majorana modes are quantitatively captured by a simple Landau-Zener description. We further simulate a Rabi-oscillation protocol in a specific qubit design with four Majorana zero modes in a single wire and quantify constraints on the timescales for performing qubit operations in this setup. Our simulations utilize a Majorana representation of the system, which greatly simplifies simulations of superconductors at the mean-field level.

scholarly journals Exotic Baryons in Chiral Soliton Models

Universe ◽  
2018 ◽  
Vol 4 (12) ◽  
pp. 142
Author(s):  
Herbert Weigel
Keyword(s):  
Canonical Quantization ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Collective Coordinates ◽  
Zero Modes ◽  
Chiral Soliton ◽  
Exotic Baryons ◽  
The Mean

We cautiously review the treatment of pentaquark exotic baryons in chiral soliton models. We consider two examples and argue that any consistent and self-contained description must go beyond the mean field approximation that only considers the classical soliton and the canonical quantization of its (would-be) zero modes via collective coordinates.

Critical phenomena: General considerations. Mean-field theory (MFT)

2021 ◽  
pp. 324-356
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Critical Temperature ◽  
Critical Phenomena ◽  
Correlation Length ◽  
Particle Physics ◽  
Mean Field ◽  
Lattice Models ◽  
Field Approximation ◽  
Phase Region ◽  
Mean Field Approximation ◽  
The Mean

This chapter is devoted to a brief review of general properties of phase transitions in macroscopic physics and, in particular in lattice models. Some of these lattice models actually appear as lattice regularizations of Euclidean (imaginary time) quantum physics theory (QFT). Most of the transitions considered in this work have the following character: spins on the lattice, or macroscopic particles in the continuum, interact through short-range forces, assumed, for simplicity, to decay exponentially. For simple systems, it is possible to find a local observable, called order parameter, whose expectation values depend on the phase in the several phase region, for example, the spin in ferromagnetic systems. In the disordered phase, the connected two-point function decreases exponentially at large distance, at a rate characterized by the correlation length (the inverse of the smallest physical mass in particle physics). In continuous transitions, the correlation length diverges at the critical temperature. Within the mean-field approximation (consistent with Landau's theory of critical phenomena), it can be shown that the singular behaviour of thermodynamic quantities at the critical temperature is universal. These properties can also be reproduced by calculating correlation functions with a perturbed Gaussian measure. It is then shown that the leading corrections to the mean-field approximation, in Ising-like systems, diverge at the critical temperature for dimensions smaller than or equal to $4$.

A continuum theory of disorder in nematic liquid crystals IV. Application to lattice models+

1980 ◽  
Vol 370 (1743) ◽  
pp. 509-521 ◽  
Keyword(s):  
Mean Field Theory ◽  
Random Phase ◽  
Mean Field ◽  
Lattice Models ◽  
Continuum Theory ◽  
Wave Theory ◽  
Approximate Theory ◽  
Secondary Importance ◽  
Nearest Neighbours ◽  
The Mean

An approximate theory of nematic disorder, reminiscent of the spin wave theory of ferromagnetic disorder, was put forward in previous papers in this series. Predictions based upon it are here compared with accurate results for two lattice models: (a) a model in which the interaction which causes molecules to align is between nearest neighbours only, which Zannoni (1979) has investigated by computer simulation, and (b) a model in which the interaction is of very long range, to which the mean field theory ofMaier & Saupe (1958,1959, i960) is applicable. At temperatures not too close to the nematic-isotropic transition temperature Tc the theory predicts the magnitude of S2 with remarkable precision for both models, though no adjustable parameters are involved. It also predicts correctly the magnitude and the range of the short-range order that is characteristic of model (a). Since some of the discrepancies that become apparent as Tc is approached can be attributed to an approximation of rather secondary importance - neglect of the effect that misalignment entropy may have on the Frank stiffness constants of a nematic - it looks as though the theory can safely be used to describe real nematics at temperatures such that S 2 exceeds, say, 0.5. A prediction that S 4 (= (P 4 (cos 0))) is equal to however, which is certainly correct for both models at very low temperatures, begins to fail, though not dramatically, when S2 reaches about 0.7. This failure is attributed to errors in the random phase approximation, to which the other results of the theory are relatively insensitive.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals The Mean-field Behavior of Processor Sharing Systems with General Job Lengths Under the SQ(d) Policy

2019 ◽  
Vol 46 (3) ◽  
pp. 54-55
Author(s):  
Thirupathaiah Vasantam ◽  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar
Keyword(s):  
Mean Field ◽  
Processor Sharing ◽  
Field Behavior ◽  
The Mean

scholarly journals The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu
Keyword(s):  
Existence Of Solutions ◽  
Particle System ◽  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Unique Existence ◽  
Interacting Particle ◽  
Microscopic Derivation ◽  
The Mean ◽  
Limit Result

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

Sign in / Sign up

Export Citation Format

Share Document