Non-equilibrium Thermodynamics and Conformal Field Theory

AbstractWe study the non-equilibrium dynamics of conformal field theory (CFT) in 1+1 dimensions with a smooth position-dependent velocity v(x) explicitly breaking translation invariance. Such inhomogeneous CFT is argued to effectively describe 1+1-dimensional quantum many-body systems with certain inhomogeneities varying on mesoscopic scales. Both heat and charge transport are studied, where, for concreteness, we suppose that our CFT has a conserved U(1) current. Based on projective unitary representations of diffeomorphisms and smooth maps in Minkowskian CFT, we obtain a recipe for computing the exact non-equilibrium dynamics in inhomogeneous CFT when evolving from initial states defined by smooth inverse-temperature and chemical-potential profiles $$\beta (x)$$ β ( x ) and $$\mu (x)$$ μ ( x ) . Using this recipe, the following exact analytical results are obtained: (i) the full time evolution of densities and currents for heat and charge transport, (ii) correlation functions for components of the energy–momentum tensor and the U(1) current as well as for any primary field, and (iii) the thermal and electrical conductivities. The latter are computed by direct dynamical considerations and alternatively using a Green–Kubo formula. Both give the same explicit expressions for the conductivities, which reveal how inhomogeneous dynamics opens up the possibility for diffusion as well as implies a generalization of the Wiedemann–Franz law to finite times within CFT.

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Non-Equilibrium Steady States in Conformal Field Theory

Annales Henri Poincaré ◽

10.1007/s00023-014-0314-8 ◽

2014 ◽

Vol 16 (1) ◽

pp. 113-161 ◽

Cited By ~ 72

Author(s):

Denis Bernard ◽

Benjamin Doyon

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Steady States ◽

Conformal Field ◽

Non Equilibrium

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Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2014/03/p03002 ◽

2014 ◽

Vol 2014 (3) ◽

pp. P03002 ◽

Cited By ~ 13

Author(s):

Benjamin Doyon ◽

Marianne Hoogeveen ◽

Denis Bernard

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Energy Flow ◽

Star Graphs ◽

Conformal Field ◽

Non Equilibrium

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A Review of Conformal Field Theory in 2D

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v6i2.1784 ◽

2014 ◽

Vol 6 (2) ◽

pp. 1079-1105

Author(s):

Rahul Nigam

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Conformal Field Theory ◽

Statistical Mechanics ◽

Critical Behavior ◽

Verma Module ◽

Virasoro Algebra ◽

Quantum Field ◽

Conformal Field ◽

Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".Â Â

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