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Siovitz I, Lannig S, Deller Y, Strobel H, Oberthaler MK, Gasenzer T. Universal Dynamics of Rogue Waves in a Quenched Spinor Bose Condensate. Phys Rev Lett 2023; 131:183402. [PMID: 37977625 DOI: 10.1103/physrevlett.131.183402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/10/2023] [Indexed: 11/19/2023]
Abstract
Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.
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Affiliation(s)
- Ido Siovitz
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Stefan Lannig
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Yannick Deller
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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Marino J, Eckstein M, Foster MS, Rey AM. Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments. Rep Prog Phys 2022; 85:116001. [PMID: 36075190 DOI: 10.1088/1361-6633/ac906c] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 09/08/2022] [Indexed: 06/15/2023]
Abstract
We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions,ϕ4quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.
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Affiliation(s)
- Jamir Marino
- Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - Martin Eckstein
- Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, United States of America
- Rice Center for Quantum Materials, Rice University, Houston, TX 77005, United States of America
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology, and Department of Physics,University of Colorado, Boulder, CO 80309, United States of America
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, United States of America
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Rodriguez-Nieva JF, Piñeiro Orioli A, Marino J. Far-from-equilibrium universality in the two-dimensional Heisenberg model. Proc Natl Acad Sci U S A 2022; 119:e2122599119. [PMID: 35787047 DOI: 10.1073/pnas.2122599119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy in a wide range. Compared to previously studied self-similar dynamics in nonequilibrium O(n) field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes that remain gapless at long times and are protected by the global SU(2) symmetry. Our predictions, which suggest a distinct nonequilibrium universality class from Bose gases and O(n) theories, are readily testable in ultracold atoms simulators of Heisenberg magnets.
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Shu YR, Jian SK, Yin S. Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time. Phys Rev Lett 2022; 128:020601. [PMID: 35089734 DOI: 10.1103/physrevlett.128.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 10/07/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
Deconfined quantum critical point (DQCP) characterizes a kind of exotic phase transition beyond the usual Landau-Ginzburg-Wilson paradigm. Here we study the nonequilibrium imaginary-time dynamics of the DQCP in the two-dimensional J-Q_{3} model. We explicitly show the deconfinement dynamic process and identify that it is the spinon confinement length, rather than the usual correlation length, that increases proportionally to the time. Moreover, we find that, in the relaxation process, the order parameters of the Néel and the valence-bond-solid orders can be controlled by different length scales, although they satisfy the same equilibrium scaling forms. A dual dynamic scaling theory is then proposed. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems. Possible realizations in foreseeable quantum computers are also discussed.
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Affiliation(s)
- Yu-Rong Shu
- School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China
| | - Shao-Kai Jian
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Shuai Yin
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
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Halimeh JC, Maghrebi MF. Quantum aging and dynamical universality in the long-range O(N→∞) model. Phys Rev E 2021; 103:052142. [PMID: 34134217 DOI: 10.1103/physreve.103.052142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
Quantum quenches to or near criticality give rise to the phenomenon of aging, manifested by glassylike dynamics at short times and far from equilibrium. The recent surge of interest in the dynamics of quantum many-body systems has rejuvenated interest in this phenomenon. Motivated by the ubiquitous long-range interactions in emerging experimental platforms, it is vital to study quantum aging in such settings. In this paper, we investigate the dynamical universality and aging in the d-dimensional O(N) model with the long-range coupling 1/x^{d+σ} and in the mean-field limit N→∞ that allows an exact treatment. An immediate consequence of long-range coupling is the emergence of nonlinear light cones. We focus on the correlation and response functions, and identify a rich scaling behavior depending on how the corresponding space-time positions are located relative to each other, via a local light cone, and to the time of the quench via a global quench light cone. We determine the initial-slip exponent that governs the short-time dependence of two-point functions. We highlight the qualitative features of aging due to the long-range coupling, in particular in the region outside the light cones. As an important consequence of long-range coupling, the correlation function decays as 1/x^{d+σ} outside the quench light cone while increasing polynomially with the total time after quench. This is while, for short-time differences, the two-time response function "equilibrates" at all distances even outside this light cone. Our analytic findings are in excellent agreement with exact numerics, and provide a useful benchmark for modern experimental platforms with long-range interactions.
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Affiliation(s)
- Jad C Halimeh
- INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy.,Kirchhoff Institute for Physics, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany.,Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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Kelly SP, Rey AM, Marino J. Effect of Active Photons on Dynamical Frustration in Cavity QED. Phys Rev Lett 2021; 126:133603. [PMID: 33861099 DOI: 10.1103/physrevlett.126.133603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 03/05/2021] [Indexed: 06/12/2023]
Abstract
We study the far-from-equilibrium dynamical regimes of a many-body spin-boson model with disordered couplings relevant for cavity QED and trapped ion experiments, using the discrete truncated Wigner approximation. We focus on the dynamics of spin observables upon varying the disorder strength and the frequency of the photons, finding that the latter can considerably alter the structure of the system's dynamical responses. When the photons evolve at a similar rate as the spins, they can induce qualitatively distinct frustrated dynamics characterized by either logarithmic or algebraically slow relaxation. The latter illustrates resilience of glassylike dynamics in the presence of active photonic degrees of freedom, suggesting that disordered quantum many-body systems with resonant photons or phonons can display a rich diagram of nonequilibrium responses, with near future applications for quantum information science.
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Affiliation(s)
- Shane P Kelly
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
| | - Ana Maria Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Jamir Marino
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
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Jian SK, Yin S, Swingle B. Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality. Phys Rev Lett 2019; 123:170606. [PMID: 31702242 DOI: 10.1103/physrevlett.123.170606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Indexed: 06/10/2023]
Abstract
We study the prethermal dynamics of the Gross-Neveu-Yukawa quantum field theory, suddenly quenched in the vicinity of a critical point. We find that the universal prethermal dynamics is controlled by two fixed points depending on the size of the quench. Besides the usual equilibrium chiral Ising fixed point for a shallow quench, a dynamical chiral Ising fixed point is identified for a deep quench. Intriguingly, the latter is a nonthermal fixed point without any equilibrium counterpart due to the participation of gapless fermionic fields. We also find that in the scaling regime controlled by the equilibrium fixed point, the initial slip exponent is rendered negative if there are enough flavors of fermions, thus providing a unique signature of fermionic prethermal dynamics. We then explore the temporal crossover between the universal scaling regimes governed by the two universality classes. Possible experimental realizations are also discussed.
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Affiliation(s)
- Shao-Kai Jian
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Shuai Yin
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- School of physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Brian Swingle
- Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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Abstract
We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.
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Affiliation(s)
- Alessio Chiocchetta
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Sebastian Diehl
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Jamir Marino
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
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Abstract
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
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Affiliation(s)
- L M Sieberer
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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Maraga A, Chiocchetta A, Mitra A, Gambassi A. Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:042151. [PMID: 26565212 DOI: 10.1103/physreve.92.042151] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Indexed: 06/05/2023]
Abstract
The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.
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Affiliation(s)
- Anna Maraga
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Alessio Chiocchetta
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Aditi Mitra
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
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