scholarly journals Bath-induced decoherence in finite-size Majorana wires at non-zero temperature

2021 ◽  
Author(s):  
Niels Breckwoldt ◽  
Thore Posske ◽  
Michael Thorwart
Keyword(s):  
Time Scale ◽  
Finite Size ◽  
Information Storage ◽  
One Dimensional ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Intermediate Time ◽  
Topological Errors ◽  
The One ◽  
Intermediate Time Scale

Abstract Braiding Majorana zero-modes around each other is a promising route towards topological quantum computing. Yet, two competing maxims emerge when implementing Majorana braiding in real systems: On the one hand, perfect braiding should be conducted adiabatically slowly to avoid non-topological errors. On the other hand, braiding must be conducted fast such that decoherence effects introduced by the environment are negligible, which are generally unavoidable in finite-size systems. This competition results in an intermediate time scale for Majorana braiding that is optimal, but generally not error-free. Here, we calculate this intermediate time scale for a T-junction of short one-dimensional topological superconductors coupled to a bosonic bath that generates fluctuations in the local electric potential, which stem from, e.g., environmental photons or phonons of the substrate. We thereby obtain boundaries for the speed of Majorana braiding with a predetermined gate fidelity. Our results emphasize the general susceptibility of Majorana-based information storage in finite-size systems and can serve as a guide for determining the optimal braiding times in future experiments.

scholarly journals Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm

2021 ◽  
Author(s):  
Niccolò Traverso Ziani ◽  
Lucia Vigliotti ◽  
Matteo Carrega ◽  
Fabio Cavaliere
Keyword(s):  
Quantum Computation ◽  
Bound States ◽  
Research Activity ◽  
One Dimensional ◽  
Majorana Bound States ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Tamm State ◽  
Topological Quantum Computation ◽  
Intense Research

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. We here study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.

scholarly journals Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1028 ◽  
Author(s):  
Alessandro Pelizzola ◽  
Marco Pretti ◽  
Francesco Puccioni
Keyword(s):  
Finite Size ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Pair Approximation ◽  
Fundamental Diagram ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The One

Dynamical transitions, already found in the high- and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz–Lebowitz–Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz–Lebowitz–Spohn model, and discuss 2 new phenomena which are peculiar to this model.

scholarly journals On monolithic supermassive stars

2020 ◽  
Vol 494 (2) ◽  
pp. 2236-2243 ◽  
Author(s):  
Tyrone E Woods ◽  
Alexander Heger ◽  
Lionel Haemmerlé
Keyword(s):  
Early Universe ◽  
Stellar Evolution ◽  
Time Scale ◽  
Main Sequence ◽  
Massive Stars ◽  
Rotating Stars ◽  
One Dimensional ◽  
General Relativistic ◽  
The One ◽  
Limiting Case

ABSTRACT Supermassive stars have been proposed as the progenitors of the massive ($\sim \!10^{9}\, \mathrm{M}_{\odot }$) quasars observed at z ∼ 7. Prospects for directly detecting supermassive stars with next-generation facilities depend critically on their intrinsic lifetimes, as well as their formation rates. We use the one-dimensional stellar evolution code kepler to explore the theoretical limiting case of zero-metallicity non-rotating stars, formed monolithically with initial masses between $10$ and $190\, \mathrm{kM}_{\odot }$. We find that stars born with masses between $\sim\! 60$ and $\sim\! 150\, \mathrm{kM}_{\odot }$ collapse at the end of the main sequence, burning stably for $\sim\! 1.5\, \mathrm{Myr}$. More massive stars collapse directly through the general relativistic instability after only a thermal time-scale of $\sim\! 3$–$4\, \mathrm{kyr}$. The expected difficulty in producing such massive thermally relaxed objects, together with recent results for currently preferred rapidly accreting formation models, suggests that such ‘truly direct’ or ‘dark’ collapses may not be typical for supermassive objects in the early Universe. We close by discussing the evolution of supermassive stars in the broader context of massive primordial stellar evolution and the possibility of supermassive stellar explosions.

scholarly journals Incompressible impulsive sloshing

2012 ◽  
Vol 708 ◽  
pp. 279-302 ◽  
Author(s):  
Peder A. Tyvand ◽  
Touvia Miloh
Keyword(s):  
Circular Cylinder ◽  
Time Scale ◽  
Hydrodynamic Force ◽  
Small Time ◽  
Surface Velocity ◽  
Leading Order ◽  
Intermediate Time ◽  
Time Expansion ◽  
Horizontal Cylinders ◽  
Intermediate Time Scale

AbstractThe incompressible impulsive time scale for inviscid liquid sloshing in open rigid containers suddenly put into motion is defined as the intermediate time scale in between the acoustic time scale and the gravitational time scale. Surge and sway boundary-value problems for incompressible impulsive sloshing in some realistic container shapes are solved analytically to the leading order in a small-time expansion. A solution is provided for two types of horizontal cylinders: a triangular cylindrical wedge and a half-filled circular cylinder. The surface velocity and the hydrodynamic force with its corresponding virtual fluid mass are calculated. The cases of constant impulsive velocity and constant impulsive acceleration are linked by transformation equations. Flows with waterline singularities are discussed, being leading-order outer flows in terms of matched asymptotic expansions.

Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

2020 ◽  
Vol 75 (2) ◽  
pp. 175-182
Author(s):  
Magdy E. Amin ◽  
Mohamed Moubark ◽  
Yasmin Amin
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Boundary Conditions ◽  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
The One ◽  
Bulk Case

AbstractThe one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

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