2014

Non-Equilibrium Conformal Field Theories with Impurities

Bernard, D., Doyon, B., Viti, J.

Understand

We present a construction of non-equilibrium steady states within conformal field theory.

These states sustain energy flows between two quantum systems, initially prepared at different temperatures, whose dynamical properties are represented by two, possibly different, conformal field theories connected through an impurity.
This construction relies on a real time formulation of conformal defect dynamics based on a field scattering picture parallelizing - but yet different from - the Euclidean formulation.
We present the basic characteristics of this formulation and give an algebraic construction of the real time scattering maps that we illustrate in the case of SU(2)-based conformal field theories.

Built on

T. Giamarchi, A.J. Millis, “Conductivity of a Luttinger liquid”, Phys. Rev. B46
1922
Earlier work this paper cites.
A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory”, Nucl. Phys.B241, 333 (1984)
1984
Earlier work this paper cites.
J. Cardy, “Conformal Invariance and Surface Critical Behavior”, Nucl. Phys. B240 [FS12], 514-532, 1984
1984
Earlier work this paper cites.
H. Castela, X. Zotos, P. Prelovsek, “Integrability and Ideal Conductance at Finite Temperatures”, Phys. Rev. Lett. 74
1995
Earlier work this paper cites.
Ph. Di Francesco, P. Mathieu, D. Senechal, “Conformal Field Theory”, Springer (New-York), 1997
1997
Earlier work this paper cites.
Y.M. Blanter, M. Buttiker, “Shot noise in mesoscopic conductors”, Phys. Rep. 336 (2000) 1
2000
Earlier work this paper cites.
D. Ruelle, “Natural non-equilibrium states in quantum statistical mechanics”, J. Stat. Phys. 98, 57 (2000)
2000
Earlier work this paper cites.
V. Jakšić and C.-A. Pillet, “On entropy production in quantum statistical mechanics”, Commun. Math. Phys. 217, 285Ð293 (2001)
2001
Earlier work this paper cites.
V.B. Petkova, J.-B. Zuber, “Generalised twisted partition functions”, Phys. Lett. B 504 (2001) 533
2001
Earlier work this paper cites.
C.-A. Pillet, “Entropy production in classical and quantum systems”, Markov Process. Relat. Fields 7, 145Ð157 (2001)
2001
Earlier work this paper cites.

Similar

D. Ruelle, “Entropy production in quantum spin systems”, Commun. Math. Phys. 224, 3Ð16 (2001)
2001
Cited alongside, same era.
R. Zwanzig,“Non-equilibrium statistical physics”, Oxford Univ. Press 2002
2002
Cited alongside, same era.
W.H. Aschbacher, C.-A. Pillet, “Non-equilibrium steady states of the XY chain”, J. Stat. Phys. 112, 1153 (2003)
2003
Cited alongside, same era.
V. Jakšić and C.-A. Pillet, “A note on the entropy production formula”, Contemp. Math. 327, 175 (2003)
2003
Cited alongside, same era.
J. Bylander, T. Duty, and P. Delsing, “Current measuring by real time counting of single electrons”, Nature 434, 361 (2005)
2005
Cited alongside, same era.
S. Gustavsson, et al, “Counting statistics of single electron transport in quantum dot”, Phys. Rev. Lett. 96, 076605 (2006)
2006
Cited alongside, same era.
J. Fuchs, M.R. Gaberdiel, I. Runkel, C. Schweigert, “Topological defects for the free boson CFT”, J. Phys. A: Math. Theor. 40 (2007) 11403
2007
Cited alongside, same era.
T. Quella, I. Runkel, G.M.T. Watts, “Reflection and transmission for conformal defects”, JHEP04 (2007) 095
2007
Cited alongside, same era.
C. Bachas, I. Brunner, “Fusion of conformal interfaces”, JHEP02 (2008) 085
2008
Cited alongside, same era.
K. Andrieux, P. Gaspard, T. Monnai, S. Tasaki, “The fluctuation theorem for currents in open quantum systems”, New J. Phys. 11 (2009), 043014
2009
Cited alongside, same era.
D. Bernard, B. Doyon, “Non-equilibrium steady-states in conformal field theory”, Ann. H. Poincare, online first, arXiv:1302.3125
Original
Cited in the paper.
D. Bernard, B. Doyon, J. Viti, “Non-equilibrium CFT (II)”, in preparation
Cited in the paper.

Then

J. Sirker, R.G. Pereira, I. Affleck, “Diffusion and Ballistic Transport in One Dimensional Quantum Systems”, Phys. Rev. Lett. 103
2009
Later among the works it cites.
D.B. Gutman, Yu. Gefen, A.D. Mirlin, “Full counting statistics of Luttinger liquid conductor”, Phys. Rev. Lett. 105, 256802 (2010)
2010
Later among the works it cites.
A. Davydov, L. Kong, I. Runkel, “Invertible defects and isomorphisms of rational CFTs”, Adv. Math. Theor. Phys. 15 (2011), 43
2011
Later among the works it cites.
T. Prosen, “Open XXZ Spin Chain “Non-equilibrium Steady State and a Strict Bound on Ballistic Transport”, Phys. Rev. Lett. 106
2011
Later among the works it cites.
D. Bernard, B. Doyon, “Energy flow in non-equilibrium conformal field theory.”, J. Phys. A 45, 362001 (2012)
2012
Later among the works it cites.
S. Jezouin et al., “Quantum Limit of Heat Flow Across a Single Electronic Channel”, Science 342, 601 (2013)
2013
Later among the works it cites.
M. Mintchev, P. Sorba, “Luttinger Liquid in Non-equilibrium Steady State”, J. Phys. A: Math. Theor. 46 (2013)
2013
Later among the works it cites.
R. Ben Sad, C.-A. Pillet, “A geometric approach to the Landauer-Bttiker formula”, J. Math. Phys. 55, 075202 (2014)
2014
Closest in time.
S. Krinner, D. Stadler, D. Husmann, J.-P. Brantut and T. Esslinger, “Observation of Quantized Conductance in Neutral Matter”, ArXiv:1404.6400, 2014
Original
2014
Closest in time.
A. De Luca, J. Viti, L. Mazza and D. Rossini, “Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm”, Phys. Rev. B 90 16 (2014)
2014
Closest in time.

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