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In this article we review the past, present, and future of the Loschmidt Echo.
“Spin Echoes”
E. L. Hahn · 1950
Earlier work this paper cites.
“Time-Reversal Experiments in Dipolar-Coupled Spin Systems”
W.-K. Rhim, A. Pines, and J. S. Waugh · 1971
Earlier work this paper cites.
“Atomic Memory”
R. G. Brewer and E. L. Hahn · 1984
Earlier work this paper cites.
“Stability of quantum motion in chaotic and regular systems”
A. Peres · 1984
Earlier work this paper cites.
“An accurate and efficient scheme for propagating the time dependent Schrödinger equation”
H. Tal-Ezer and R. Kosloff · 1984
Earlier work this paper cites.
“Principles of Magnetic Resonance”
C. P. Slichter · 1990
Earlier work this paper cites.
“Polarization echoes in NMR”
S. Zhang, B. H. Meier, and R. R. Ernst · 1992
Earlier work this paper cites.
“Quantum Dynamical Echoes in the Spin Diffusion in Mesoscopic Systems”
H. M. Pastawski, P. R. Levstein, and G. Usaj · 1995
Earlier work this paper cites.
“Computer simulation of quantum phenomena in nanoscale devices”
H. De Raedt · 1996
Earlier work this paper cites.
“Time-resolved observation of spin waves in a linear chain of nuclear spins”
Z. L. Mádi, B. Brutscher, T. Schulte-Herbrüggen, R. Brüschweiler, and R. R. Ernst · 1997
Earlier work this paper cites.
“Attenuation of polarization echoes in nuclear magnetic resonance: A study of the emergence of dynamical irreversibility in many-body quantum systems”
P. R. Levstein, G. Usaj, and H. M. Pastawski · 1998
Earlier work this paper cites.
“Gaussian to exponential crossover in the attenuation of polarization echoes in NMR”
G. Usaj, H. M. Pastawski, and P. R. Levstein · 1998
Earlier work this paper cites.
“Time-Reversed Acoustics”
M. Fink · 1999
Earlier work this paper cites.
“A nuclear magnetic resonance answer to the Boltzmann-Loschmidt controversy?”
H. M. Pastawski, P. R. Levstein, G. Usaj, J. Raya, and J. Hirschinger · 2000
Earlier work this paper cites.
“Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo”
Ph. Jacquod, P. G. Silvestrov, and C. W. J. Beenakker · 2001
Earlier work this paper cites.
“Environment-Independent Decoherence Rate in Classically Chaotic Systems”
R. A. Jalabert and H. M. Pastawski · 2001
Earlier work this paper cites.
“Sub-Planck structure in phase space and its relevance for quantum decoherence”
W. H. Zurek · 2001
Earlier work this paper cites.
“Gaussian Decoherence and Gaussian Echo from Spin Environments”
W. H. Zurek, F. M. Cucchietti, and J. P. Paz · 2001
Earlier work this paper cites.
“Quantum-classical correspondence in perturbed chaotic systems”
G. Benenti and G. Casati · 2002
Earlier work this paper cites.
“Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems”
N. R. Cerruti and S. Tomsovic · 2002
Earlier work this paper cites.
“Measuring the Lyapunov exponent using quantum mechanics”
F. M. Cucchietti, C. H. Lewenkopf, E. R. Mucciolo, H. M. Pastawski, and R. O. Vallejos · 2002
Earlier work this paper cites.
“Decoherence as decay of the Loschmidt echo in a Lorentz gas”
F. M. Cucchietti, H. M. Pastawski, and D. A. Wisniacki · 2002
Earlier work this paper cites.
“General relation between quantum ergodicity and fidelity of quantum dynamics”
T. Prosen · 2002
Earlier work this paper cites.
“Stability of quantum motion and correlation decay”
T. Prosen and M. Žnidarič · 2002
Earlier work this paper cites.
“Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states”
D. A. Wisniacki and D. Cohen · 2002
Earlier work this paper cites.
“Loschmidt echo and Lyapunov exponent in a quantum disordered system”
Y. Adamov, I. V. Gornyi, and A. D. Mirlin · 2003
Earlier work this paper cites.
“Echo Spectroscopy and Quantum Stability of Trapped Atoms”
M. F. Andersen, A. Kaplan, and N. Davidson · 2003
Earlier work this paper cites.
“Stability of classical chaotic motion under a system’s perturbations”
G. Benenti, G. Casati, and G. Veble · 2003
Earlier work this paper cites.
“A uniform approximation for the fidelity in chaotic systems”
N. R. Cerruti and S. Tomsovic · 2003
Earlier work this paper cites.
“Decoherence and the Loschmidt Echo”
F. M. Cucchietti, D. A. R. Dalvit, J. P. Paz, and W. H. Zurek · 2003
Earlier work this paper cites.
“Echoes in classical dynamical systems”
B. Eckhardt · 2003
Earlier work this paper cites.
“Classical Decays in Decoherent Quantum Maps”
I. García-Mata, M. Saraceno, and M. E. Spina · 2003
Cited alongside, same era.
“Anomalous power law of quantum reversibility for classically regular dynamics”
Ph. Jacquod, I. Adagideli, and C. W. J. Beenakker · 2003
Cited alongside, same era.
“Coda-Wave Interferometry in Finite Solids: Recovery of P P -to- S S Conversion Rates in an Elastodynamic Billiard”
O. I. Lobkis and R. L. Weaver · 2003
Cited alongside, same era.
“Quantum freeze of fidelity decay for a class of integrable dynamics”
T. Prosen and M. Žnidarič · 2003
Cited alongside, same era.
“Recurrence of fidelity in nearly integrable systems”
R. Sankaranarayanan and A. Lakshminarayan · 2003
Cited alongside, same era.
“Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics”
P. G. Silvestrov, J. Tworzydlo, and C. W. J. Beenakker · 2003
“Time evolution of multiple quantum coherences in NMR”
C. M. Sánchez, H. M. Pastawski, and P. R. Levstein · 2007
Later among the works it cites.
“Stability of quantum motion in regular systems: A uniform semiclassical approach”
W. G. Wang, G. Casati, and B. Li · 2007
Later among the works it cites.
“Semiclassical Theory of Time-Reversal Focusing”
H. L. Calvo, R. A. Jalabert, and H. M. Pastawski · 2008
Later among the works it cites.
“Loschmidt echo for local perturbations: non-monotonic cross-over from the Fermi-golden-rule to the escape-rate regime”
A. Goussev, D. Waltner, K. Richter, and R. A. Jalabert · 2008
Later among the works it cites.
“Algebraic Fidelity Decay for Local Perturbations”
R. Höhmann, U. Kuhl, and H.-J. Stöckmann · 2008
Later among the works it cites.
“Surprising Relations between Parametric Level Correlations and Fidelity Decay”
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Cited alongside, same era.
“Semiclassical evaluation of quantum fidelity”
J. Vaníček and E. J. Heller · 2003
Cited alongside, same era.
“Short-time decay of the Loschmidt echo”
D. A. Wisniacki · 2003
Cited alongside, same era.
“Decoherence, einselection, and the quantum origins of the classical”
W. H. Zurek · 2003
Cited alongside, same era.
“Revivals of coherence in chaotic atom-optics billiards”
M. F. Andersen, T. Grünzweig, A. Kaplan, and N. Davidson · 2004
Cited alongside, same era.
“Universality of the Lyapunov regime for the Loschmidt echo”
F. M. Cucchietti, H. M. Pastawski, and R. A. Jalabert · 2004
Cited alongside, same era.
“Spin projection chromatography”
E. P. Danieli, H. M. Pastawski, and P. R. Levstein · 2004
Cited alongside, same era.
H. Kohler, I. E. Smolyarenko, C. Pineda, T. Guhr, F. Leyvraz, and T. H. Seligman · 2008
Later among the works it cites.
“Fidelity Decay in Trapped Bose-Einstein Condensates”
G. Manfredi and P.-A. Hervieux · 2008
Later among the works it cites.
“Cooling by Time Reversal of Atomic Matter Waves”
J. Martin, B. Georgeot, and D. L. Shepelyansky · 2008
Later among the works it cites.
“Loschmidt echo and the local density of states”
N. Ares and D. A. Wisniacki · 2009
Later among the works it cites.
“Probing Localization in Absorbing Systems via Loschmidt Echos”
J. D. Bodyfelt, M. C. Zheng, T. Kottos, U. Kuhl, and H.-J. Stöckmann · 2009
Later among the works it cites.
“Long-time saturation of the Loschmidt echo in quantum chaotic billiards”
M. Gutiérrez and A. Goussev · 2009
Later among the works it cites.
“Effective one-body dynamics in multiple-quantum NMR experiments”
E. Rufeil-Fiori, C. M. Sánchez, F. Y. Oliva, H. M. Pastawski, and P. R. Levstein · 2009
Later among the works it cites.
“NMR Loschmidt echoes as quantifiers of decoherence in interacting spin systems”
C. M. Sánchez, P. R. Levstein, R. H. Acosta, and A. K. Chattah · 2009
Later among the works it cites.
“Sensor based on extending the concept of fidelity to classical waves”
B. T. Taddese, J. Hart, T. M. Antonsen, E. Ott, and S. M. Anlage · 2009
Later among the works it cites.
“Observation of Saturation of Fidelity Decay with an Atom Interferometer”
S. Wu, A. Tonyushkin, and M. G. Prentiss · 2009
Later among the works it cites.
“Discrepancies between decoherence and the Loschmidt echo”
B. Casabone, I. García-Mata, and D. A. Wisniacki · 2010
Later among the works it cites.
“Quantum corrections to fidelity decay in chaotic systems”
B. Gutkin, D. Waltner, M. Gutiérrez, J. Kuipers, and K. Richter · 2010
Later among the works it cites.
“Microwave fidelity studies by varying antenna coupling”
B. Köber, U. Kuhl, H.-J. Stöckmann, T. Gorin, D. V. Savin, and T. H. Seligman · 2010
Later among the works it cites.
“Lyapunov decoherence rate in classically chaotic systems”
M. V. S. Bonança · 2011
Later among the works it cites.
“Semiclassical approach to fidelity amplitude”
I. García-Mata, R. O. Vallejos, and D. A. Wisniacki · 2011
Later among the works it cites.
“Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime”
I. García-Mata and D. A. Wisniacki · 2011
Later among the works it cites.
“Nonmonotonic short-time decay of the Loschmidt echo in quasi-one-dimensional systems”
A. Goussev · 2011
Later among the works it cites.
“Fidelity decay for local perturbations: Microwave evidence for oscillating decay exponents”
B. Köber, U. Kuhl, H.-J. Stöckmann, A. Goussev, and K. Richter · 2011
Later among the works it cites.
“Parametric correlations versus fidelity decay: The symmetry breaking case”
H. Kohler, T. Nagao, and H.-J. Stöckmann · 2011
Later among the works it cites.
“Quantum chaos of a mixed open system of kicked cold atoms”
Y. Krivolapov, S. Fishman, E. Ott, and T. M. Antonsen · 2011
Later among the works it cites.
“Experimental characterization of coherent magnetization transport in a one-dimensional spin system”
C. Ramanathan, P. Cappellaro, L. Viola, and D. G. Cory · 2011
Later among the works it cites.
“Experimental observation of Loschmidt time reversal of a Quantum Chaotical System”
A. Ullah and M. D. Hoogerland · 2011
Later among the works it cites.
“Efficiency and accuracy of numerical solutions to the time-dependent Schrödinger equation”
W. van Dijk, J. Brown, and K. Spyksma · 2011
Later among the works it cites.
“Initial-value representation for the Loschmidt echo”
E. Zambrano and A. M. Ozorio de Almeida · 2011
Later among the works it cites.
“Fidelity for kicked atoms with gravity near a quantum resonance”
R. Dubertrand, I. Guarneri, and S. Wimberger · 2012
Closest in time.
“Fidelity and level correlations in the transition from regularity to chaos”
H. Kohler and C. Recher · 2012
Closest in time.