scholarly journals Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Frederik Skovbo Møller ◽  
Jörg Schmiedmayer
Keyword(s):  
Open Source ◽  
Integrable Model ◽  
Integrable Models ◽  
Field Release ◽  
Generalized Hydrodynamics ◽  
Xxz Chain ◽  
Newton’S Cradle ◽  
Intuitive Interface

We present an open-source Matlab framework, titled iFluid, for simulating the dynamics of integrable models using the theory of generalized hydrodynamics (GHD). The framework provides an intuitive interface, enabling users to define and solve problems in a few lines of code. Moreover, iFluid can be extended to encompass any integrable model, and the algorithms for solving the GHD equations can be fully customized. We demonstrate how to use iFluid by solving the dynamics of three distinct systems: (i) The quantum Newton's cradle of the Lieb-Liniger model, (ii) a gradual field release in the XXZ-chain, and (iii) a partitioning protocol in the relativistic sinh-Gordon model.

Fundamental issues with open source software development (originally published in Volume 9, Number 4, April 2004)

First Monday ◽  
2005 ◽  
Author(s):  
Michelle Levesque
Keyword(s):  
Software Development ◽  
Open Source ◽  
Open Source Software ◽  
Interface Design ◽  
General Public ◽  
Development Trend ◽  
Solid Core ◽  
Open Source Software Development ◽  
Intended Audience ◽  
Intuitive Interface

Despite the growing success of the Open Source movement, most of the general public continues to feel that Open Source software is inaccessible to them. This paper discusses five fundamental problems with the current Open Source software development trend, explores why these issues are holding the movement back, and offers solutions that might help overcome these problems. The lack of focus on user interface design causes users to prefer proprietary software’s more intuitive interface. Open Source software tends to lack the complete and accessible documentation that retains users. Developers focus on features in their software, rather than ensuring that they have a solid core. Open Source programmers also tend to program with themselves as an intended audience, rather than the general public. Lastly, there is a widely known stubbornness by Open Source programmers in refusing to learn from what lessons proprietary software has to offer. If Open Source software wishes to become widely used and embraced by the general public, all five of these issues will have to be overcome.

scholarly journals Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Márton Mestyán ◽  
Vincenzo Alba
Keyword(s):  
Molecular Dynamics ◽  
Scaling Limit ◽  
Dynamics Simulation ◽  
Full Time ◽  
Large Space ◽  
Time Dynamics ◽  
Generalized Hydrodynamics ◽  
Analytical Results ◽  
Xxz Chain ◽  
Quantum Quenches

We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb-Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

scholarly journals The spin Drude weight of the XXZ chain and generalized hydrodynamics

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Andrew Urichuk ◽  
Yahya Oez ◽  
Andreas Klümper ◽  
Jesko Sirker
Keyword(s):  
Free Energy ◽  
Spin Current ◽  
Proper Treatment ◽  
Operator Expression ◽  
Expectation Value ◽  
Generalized Hydrodynamics ◽  
Xxz Chain ◽  
Matrix Eigenvalues ◽  
Drude Weight ◽  
The One

Based on a generalized free energy we derive exact thermodynamic Bethe ansatz formulas for the expectation value of the spin current, the spin current-charge, charge-charge correlators, and consequently the Drude weight. These formulas agree with recent conjectures within the generalized hydrodynamics formalism. They follow, however, directly from a proper treatment of the operator expression of the spin current. The result for the Drude weight is identical to the one obtained 20 years ago based on the Kohn formula and TBA. We numerically evaluate the Drude weight for anisotropies \Delta=\cos(\gamma)Δ=cos(γ) with \gamma = \pi n/mγ=πn/m, n\leq mn≤m integer and coprime. We prove, furthermore, that the high-temperature asymptotics for general \gamma=\pi n/mγ=πn/m—obtained by analysis of the quantum transfer matrix eigenvalues—agrees with the bound which has been obtained by the construction of quasi-local charges.

ZERO CURVATURE CONDITION AND 2D GRAVITY THEORIES

1992 ◽  
Vol 07 (15) ◽  
pp. 3447-3472 ◽  
Author(s):  
A. DAS ◽  
W.-J. HUANG ◽  
S. ROY
Keyword(s):  
Current Algebra ◽  
2D Gravity ◽  
Integrable Model ◽  
Integrable Models ◽  
Operator Product ◽  
Curvature Condition ◽  
Kdv Hierarchy ◽  
Zero Curvature ◽  
Anomaly Equation ◽  
Gravity Theories

We propose interpreting the zero curvature condition associated with an integrable model as an anomaly equation. This can lead to the WZWN action and the associated current algebra quite readily and clarifies further the connections found between the integrable models and 2D gravity theories. We analyze, in detail, the cases SL (2, R) (KdV hierarchy), OSp (2/1) (sKdV hierarchy) and SL (3, R) (Boussinesq hierarchy) and obtain the operator product expansions of the appropriate fields. We also make some observations on the generalization of our method to SL (n, R).

scholarly journals Two Expanding Integrable Models of the Geng-Cao Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiurong Guo ◽  
Yufeng Zhang ◽  
Xuping Zhang
Keyword(s):  
Heat Equation ◽  
Lie Algebras ◽  
Burgers Equation ◽  
Integrable Model ◽  
Integrable Models ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Generalized Burgers Equation ◽  
Integrable Couplings ◽  
Integrable Coupling

As far as linear integrable couplings are concerned, one has obtained some rich and interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures of the two expanding integrable models are obtained by employing the variational identity and the trace identity, respectively.

Open-Source Online Knowledge Portals for Education

2011 ◽  
pp. 684-688
Author(s):  
Phillip Olla ◽  
Rod Crider
Keyword(s):  
Open Source ◽  
Management Systems ◽  
Course Management Systems ◽  
Software System ◽  
Course Management ◽  
E Learning ◽  
Intuitive Interface

The open-source community has created a broad suite of educational and e-learning course management systems (CMS) referred to as educational knowledge portals (EKP). An EKP is a software system designed to aid instructors in the management of online educational courses for their students, especially by helping teachers and learners with course administration. These systems make it possible for a course designer to present to students, through a single, consistent, and intuitive interface, all the components required for a course of education or training.

scholarly journals Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Gabriele Perfetto ◽  
Benjamin Doyon
Keyword(s):  
Generating Function ◽  
Large Deviation ◽  
Integrable Model ◽  
Exact Formula ◽  
Many Body ◽  
Initial State ◽  
Cumulant Generating Function ◽  
Generalized Hydrodynamics ◽  
Interacting Systems ◽  
Dynamical Fluctuations

We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.

scholarly journals Review of the London Stage Database

2020 ◽  
Vol 10 (2) ◽  
Author(s):  
Fiona Ritchie
Keyword(s):  
Eighteenth Century ◽  
Open Access ◽  
Open Source ◽  
Search Function ◽  
New Directions ◽  
The 1960S ◽  
Intuitive Interface ◽  
London Stage ◽  
The Way

The London Stage Database is an open-access and open-source website that digitises the performance records contained in the print volumes of the London Stage, published in the 1960s. The database's flexible search function and intuitive interface open up new directions in research and will change the way we think about eighteenth-century theatre.

scholarly journals Preparing exact eigenstates of the open XXZ chain on a quantum computer

2021 ◽  
Author(s):  
John S. Van Dyke ◽  
Edwin Barnes ◽  
Sophia Economou ◽  
Rafael I Nepomechie
Keyword(s):  
Spin Chain ◽  
Quantum Computer ◽  
Success Probability ◽  
Integrable Model ◽  
Quantum Algorithm ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Real Solutions ◽  
Xxz Chain ◽  
Bethe Equations

Abstract The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of (L M) 2M M! terms, the algorithm requires L + M2+ 2M qubits.

A COMMENT ON THE HAMILTON FORMALISM FOR NONLINEAR INTEGRABLE MODELS

1993 ◽  
Vol 08 (20) ◽  
pp. 1891-1899
Author(s):  
EI-ICHIRO KAWAI
Keyword(s):  
Integrable Model ◽  
Integrable Models ◽  
Symplectic Structures ◽  
Infinite Dimensional ◽  
Hamilton Formalism

It is clarified that by taking dual symplectic structures into account in an infinite-dimensional phase manifold, at least one of which must be nonlinear, induces a completely unique nonlinear integrable model.

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