Analytical techniques for linear response formula of equilibrium states

2020 ◽  
Vol 30 (1) ◽  
pp. 013134 ◽  
Author(s):  
Armando Castro
Keyword(s):  
Linear Response ◽  
Analytical Techniques ◽  
Equilibrium States ◽  
Response Formula

scholarly journals Alternative proofs of linear response for piecewise expanding unimodal maps

2009 ◽  
Vol 30 (1) ◽  
pp. 1-20 ◽  
Author(s):  
VIVIANE BALADI ◽  
DANIEL SMANIA
Keyword(s):  
Linear Response ◽  
Higher Dimensions ◽  
Higher Order ◽  
Independent Interest ◽  
Brute Force ◽  
Original Proof ◽  
Srb Measure ◽  
Unimodal Maps ◽  
Singular Terms ◽  
Response Formula

AbstractWe give two new proofs that the Sinai–Ruelle–Bowen (SRB) measure t↦μt of a C2 path ft of unimodal piecewise expanding C3 maps is differentiable at 0 if ft is tangent to the topological class of f0. The arguments are more conceptual than the original proof of Baladi and Smania [Linear response formula for piecewise expanding unimodal maps. Nonlinearity21 (2008), 677–711], but require proving Hölder continuity of the infinitesimal conjugacy α (a new result, of independent interest) and using spaces of bounded p-variation. The first new proof gives differentiability of higher order of ∫ ψ dμt if ft is smooth enough and stays in the topological class of f0 and if ψ is smooth enough (a new result). In addition, this proof does not require any information on the decomposition of the SRB measure into regular and singular terms, making it potentially amenable to extensions to higher dimensions. The second new proof allows us to recover the linear response formula (i.e. the formula for the derivative at 0) obtained by Baladi and Smania, by an argument more conceptual than the ‘brute force’ cancellation mechanism used by Baladi and Smania.

Ruelle's linear response formula, ensemble adjoint schemes and Lévy flights

Nonlinearity ◽  
2004 ◽  
Vol 17 (5) ◽  
pp. 1867-1889 ◽  
Author(s):  
G L Eyink ◽  
T W N Haine ◽  
D J Lea
Keyword(s):  
Linear Response ◽  
Lévy Flights ◽  
Levy Flights ◽  
Response Formula

scholarly journals Linear response formula for piecewise expanding unimodal maps

Nonlinearity ◽  
2008 ◽  
Vol 21 (4) ◽  
pp. 677-711 ◽  
Author(s):  
Viviane Baladi ◽  
Daniel Smania
Keyword(s):  
Linear Response ◽  
Unimodal Maps ◽  
Response Formula

scholarly journals Linear-response formula for finite-frequency thermal conductance of open systems

2011 ◽  
Vol 83 (1) ◽  
Author(s):  
Abhishek Dhar ◽  
Onuttom Narayan ◽  
Anupam Kundu ◽  
Keiji Saito
Keyword(s):  
Linear Response ◽  
Open Systems ◽  
Thermal Conductance ◽  
Finite Frequency ◽  
Response Formula

Hydrodynamics

2021 ◽  
pp. 49-66
Author(s):  
Robert W. Batterman
Keyword(s):  
Correlation Functions ◽  
Linear Response ◽  
Order Parameters ◽  
Equilibrium States ◽  
Conserved Quantities ◽  
Many Body ◽  
Hydrodynamic Description ◽  
Relative Autonomy ◽  
Many Body Systems ◽  
The Continuum

This chapter begins the argument that the best way to understand the relations of relative autonomy between theories at different scales is through a mesoscale hydrodynamic description of many-body systems. It focuses on the evolution of conserved quantities of those systems in near, but out of equilibrium states. A relatively simple example is presented of a system of spins where the magnetization is the conserved quantity of interest. The chapter introduces the concepts of order parameters, of local quantities, and explains why we should be focused on the gradients of densities that inhabit the mesoscale between the scale of the continuum and that of the atomic. It introduces the importance of correlation functions and linear response.

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