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Diezemann G. Nonlinear response theory for Markov processes. IV. The asymmetric double-well potential model revisited. Phys Rev E 2022; 106:064122. [PMID: 36671146 DOI: 10.1103/physreve.106.064122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
The dielectric response of noninteracting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double-well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double-well potential model does not follow the Langevin function and only in the linear regime are the standard results recovered. If a finite asymmetry is assumed, then the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and fifth-order responses. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, then we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similarly to the two-state model for high barriers. For small barriers no clear-cut timescale separation between the barrier crossing process and the intrawell relaxation exists and the model exhibits a number of timescales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intrawell transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intrawell transitions play only a role at the lowest temperatures.
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Affiliation(s)
- Gregor Diezemann
- Department Chemie, Johannes Gutenberg Universität Mainz, 55128 Mainz, Germany
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Speck T. Modeling non-linear dielectric susceptibilities of supercooled molecular liquids. J Chem Phys 2021; 155:014506. [PMID: 34241396 DOI: 10.1063/5.0056657] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Advances in high-precision dielectric spectroscopy have enabled access to non-linear susceptibilities of polar molecular liquids. The observed non-monotonic behavior has been claimed to provide strong support for theories of dynamic arrest based on the thermodynamic amorphous order. Here, we approach this question from the perspective of dynamic facilitation, an alternative view focusing on emergent kinetic constraints underlying the dynamic arrest of a liquid approaching its glass transition. We derive explicit expressions for the frequency-dependent higher-order dielectric susceptibilities exhibiting a non-monotonic shape, the height of which increases as temperature is lowered. We demonstrate excellent agreement with the experimental data for glycerol, challenging the idea that non-linear response functions reveal correlated relaxation in supercooled liquids.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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Shen HZ, Xu S, Zhou YH, Yi XX. System susceptibility and bound-states in structured reservoirs. OPTICS EXPRESS 2019; 27:31504-31521. [PMID: 31684385 DOI: 10.1364/oe.27.031504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Accepted: 09/16/2019] [Indexed: 06/10/2023]
Abstract
We propose a formulation to obtain the exact susceptibility for system arbitrary operators to the external fields by means of the whole-system Hamiltonian (system plus reservoir) diagonalization methods, where the dissipative effects directly reflect the nature of the structured non-Markovian reservoir. This treatment does not make the Born-Markovian approximation in structured non-Markovian reservoir. The relations between linear response function and bound-states for the system as well as structured reservoir are found, which shows the photon bound-states and continuous energy spectrum can be readout from the susceptibility, respectively. These results are then used to examine the validity of second-order Born-Markovian approximation, where we find interesting features (e.g., bound-states) are lost in the approximate treatments for open systems. We study the dependence of the response function on the type (spectrum density) of interaction between the system and structured reservoir. We also give the physical reasons behind the disappearance of the bound-states in the approximation method. Finally, these results are also extended to a more general quantum network involving an arbitrary number of coupled-bosonic system without rotating-wave approximation. The presented results might open a new door to understand the linear response and the energy spectrum for non-Markovian open systems with structured reservoirs.
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Richert R. Perspective: Nonlinear approaches to structure and dynamics of soft materials. J Chem Phys 2018; 149:240901. [DOI: 10.1063/1.5065412] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Ranko Richert
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287, USA and I. Physikalisches Institut, Universität Göttingen, D-37077 Göttingen, Germany
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Shen HZ, Xu S, Li H, Wu SL, Yi XX. Linear response theory for periodically driven systems with non-Markovian effects. OPTICS LETTERS 2018; 43:2852-2855. [PMID: 29905706 DOI: 10.1364/ol.43.002852] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
In the linear response theory, it is well known that the response of a quantum system to an external perturbation described by the susceptibility is formulated in the Schrödinger picture. The theory might apply to open quantum systems (or Floquet systems); however, it has ignored the non-Markovian effect in almost all works so far. In this Letter, we propose a new method to address those issues by introducing Heisenberg operators to derive an exact susceptibility for the non-Markovian Floquet periodic driving system. The susceptibility includes all the influences of the environment on the Floquet system. We will show that the susceptibility connects closely to the structure of the Floquet energy spectrum of the whole system (system plus environment). Moreover, we can read out Floquet bound states in the first Brillouin zone of the whole system from the susceptibility. The presented results may find applications in quantum engineering with open systems following modulated periodic evolution in quantum optics.
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Gadige P, Albert S, Michl M, Bauer T, Lunkenheimer P, Loidl A, Tourbot R, Wiertel-Gasquet C, Biroli G, Bouchaud JP, Ladieu F. Unifying different interpretations of the nonlinear response in glass-forming liquids. Phys Rev E 2018; 96:032611. [PMID: 29346923 DOI: 10.1103/physreve.96.032611] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2017] [Indexed: 11/07/2022]
Abstract
This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005)PRBMDO1098-012110.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.
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Affiliation(s)
- P Gadige
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - S Albert
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - M Michl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - Th Bauer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - P Lunkenheimer
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - A Loidl
- Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - R Tourbot
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - C Wiertel-Gasquet
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - G Biroli
- IPhT, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 774, 91191 Gif-sur-Yvette Cedex, France.,LPS, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
| | - J-P Bouchaud
- Capital Fund Management, 23 Rue de l'Université, 75007 Paris, France
| | - F Ladieu
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
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