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Keshavamurthy S. Dynamical Tunneling in More than Two Degrees of Freedom. ENTROPY (BASEL, SWITZERLAND) 2024; 26:333. [PMID: 38667887 PMCID: PMC11049088 DOI: 10.3390/e26040333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 04/08/2024] [Accepted: 04/10/2024] [Indexed: 04/28/2024]
Abstract
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose-Einstein condensates trapped in optical lattices.
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Affiliation(s)
- Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India
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2
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Liu LR, Rosenberg D, Changala PB, Crowley PJD, Nesbitt DJ, Yao NY, Tscherbul TV, Ye J. Ergodicity breaking in rapidly rotating C 60 fullerenes. Science 2023; 381:778-783. [PMID: 37590361 DOI: 10.1126/science.adi6354] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Accepted: 06/23/2023] [Indexed: 08/19/2023]
Abstract
Ergodicity, the central tenet of statistical mechanics, requires an isolated system to explore all available phase space constrained by energy and symmetry. Mechanisms for violating ergodicity are of interest for probing nonequilibrium matter and protecting quantum coherence in complex systems. Polyatomic molecules have long served as a platform for probing ergodicity breaking in vibrational energy transport. Here, we report the observation of rotational ergodicity breaking in an unprecedentedly large molecule, 12C60, determined from its icosahedral rovibrational fine structure. The ergodicity breaking occurs well below the vibrational ergodicity threshold and exhibits multiple transitions between ergodic and nonergodic regimes with increasing angular momentum. These peculiar dynamics result from the molecule's distinctive combination of symmetry, size, and rigidity, highlighting its relevance to emergent phenomena in mesoscopic quantum systems.
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Affiliation(s)
- Lee R Liu
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Dina Rosenberg
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - P Bryan Changala
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | | | - David J Nesbitt
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Department of Chemistry, University of Colorado, Boulder, CO 80309, USA
| | - Norman Y Yao
- Department of Physics, Harvard University, Cambridge, MA 02135, USA
| | | | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
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3
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Lotshaw PC, Kellman ME. Asymmetric temperature equilibration with heat flow from cold to hot in a quantum thermodynamic system. Phys Rev E 2021; 104:054101. [PMID: 34942741 DOI: 10.1103/physreve.104.054101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 09/28/2021] [Indexed: 11/07/2022]
Abstract
A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to "thermal equilibrium" at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy S_{univ}^{Q} for a pure state "universe" continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account ΔS_{univ}^{Q}≥0 holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease ΔS^{vN}<0 on the way to the asymmetric equilibrium.
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Affiliation(s)
- Phillip C Lotshaw
- Institute for Fundamental Science, Materials Science Institute, and Department of Chemistry and Biochemistry, University of Oregon Eugene, Oregon 97403, USA and Quantum Computational Sciences Group, Oak Ridge National Laboratory and Oak Ridge, Tennessee 37830, USA
| | - Michael E Kellman
- Institute for Fundamental Science, Materials Science Institute, and Department of Chemistry and Biochemistry, University of Oregon and Eugene, Oregon 97403, USA
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Gupta S, Pal D. Clusters of hairpins induce intrinsic transcription termination in bacteria. Sci Rep 2021; 11:16194. [PMID: 34376740 PMCID: PMC8355165 DOI: 10.1038/s41598-021-95435-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2020] [Accepted: 07/20/2021] [Indexed: 01/13/2023] Open
Abstract
Intrinsic transcription termination (ITT) sites are currently identified by locating single and double-adjacent RNA hairpins downstream of the stop codon. ITTs for a limited number of genes/operons in only a few bacterial genomes are currently known. This lack of coverage is a lacuna in the existing ITT inference methods. We have studied the inter-operon regions of 13 genomes covering all major phyla in bacteria, for which good quality public RNA-seq data exist. We identify ITT sites in 87% of cases by predicting hairpin(s) and validate against 81% of cases for which the RNA-seq derived sites could be calculated. We identify 72% of these sites correctly, with 98% of them located ≤ 80 bases downstream of the stop codon. The predicted hairpins form a cluster (when present < 15 bases) in two-thirds of the cases, the remaining being single hairpins. The largest number of clusters is formed by two hairpins, and the occurrence decreases exponentially with an increasing number of hairpins in the cluster. Our study reveals that hairpins form an effective ITT unit when they act in concert in a cluster. Their pervasiveness along with single hairpin terminators corroborates a wider utilization of ITT mechanisms for transcription control across bacteria.
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Affiliation(s)
- Swati Gupta
- Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, Karnataka, 560012, India
| | - Debnath Pal
- Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, Karnataka, 560012, India.
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Kalantar N, Agarwalla BK, Segal D. On the definitions and simulations of vibrational heat transport in nanojunctions. J Chem Phys 2020; 153:174101. [PMID: 33167626 DOI: 10.1063/5.0027414] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Thermal transport through nanosystems is central to numerous processes in chemistry, material sciences, and electrical and mechanical engineering, with classical molecular dynamics as the key simulation tool. Here, we focus on thermal junctions with a molecule bridging two solids that are maintained at different temperatures. The classical steady state heat current in this system can be simulated in different ways, either at the interfaces with the solids, which are represented by thermostats, or between atoms within the conducting molecule. We show that while the latter, intramolecular definition feasibly converges to the correct limit, the molecule-thermostat interface definition is more challenging to converge to the correct result. The problem with the interface definition is demonstrated by simulating heat transport in harmonic and anharmonic one-dimensional chains illustrating unphysical effects such as thermal rectification in harmonic junctions.
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Affiliation(s)
- Na'im Kalantar
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
| | - Dvira Segal
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
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Karmakar S, Keshavamurthy S. Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective. Phys Chem Chem Phys 2020; 22:11139-11173. [DOI: 10.1039/d0cp01413c] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.
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Affiliation(s)
- Sourav Karmakar
- Department of Chemistry
- Indian Institute of Technology
- Kanpur
- India
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Lotshaw PC, Kellman ME. Simulating quantum thermodynamics of a finite system and bath with variable temperature. Phys Rev E 2019; 100:042105. [PMID: 31770971 DOI: 10.1103/physreve.100.042105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2019] [Indexed: 11/07/2022]
Abstract
We construct a finite bath with variable temperature for quantum thermodynamic simulations in which heat flows between a system S and the bath environment E in time evolution of an initial SE pure state. The bath consists of harmonic oscillators that are not necessarily identical. Baths of various numbers of oscillators are considered; a bath with five oscillators is used in the simulations. The bath has a temperaturelike level distribution. This leads to definition of a system-environment microcanonical temperature T_{SE}(t) which varies with time. The quantum state evolves toward an equilibrium state which is thermal-like, but there is significant deviation from the ordinary energy-temperature relation that holds for an infinite quantum bath, e.g., an infinite system of identical oscillators. There are also deviations from the Einstein quantum heat capacity. The temperature of the finite bath is systematically greater for a given energy than the infinite bath temperature, and asymptotically approaches the latter as the number of oscillators increases. It is suggested that realizations of these finite-size effects may be attained in computational and experimental dynamics of small molecules.
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Affiliation(s)
- Phillip C Lotshaw
- Institute of Theoretical Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA
| | - Michael E Kellman
- Institute of Theoretical Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA
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Leitner DM, Pandey HD, Reid KM. Energy Transport across Interfaces in Biomolecular Systems. J Phys Chem B 2019; 123:9507-9524. [DOI: 10.1021/acs.jpcb.9b07086] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- David M. Leitner
- Department of Chemistry, University of Nevada, Reno, Nevada 89557, United States
| | - Hari Datt Pandey
- Department of Chemistry, University of Nevada, Reno, Nevada 89557, United States
| | - Korey M. Reid
- Department of Chemistry, University of Nevada, Reno, Nevada 89557, United States
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Chaotic Dynamics in a Quantum Fermi-Pasta-Ulam Problem. ENTROPY 2019; 21:e21010051. [PMID: 33266767 PMCID: PMC7514158 DOI: 10.3390/e21010051] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Revised: 12/28/2018] [Accepted: 01/08/2019] [Indexed: 11/30/2022]
Abstract
We investigate the emergence of chaotic dynamics in a quantum Fermi—Pasta—Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed.
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