Tunnel splittings for one-dimensional potential wells revisited

Garg, Anupam

doi:10.1119/1.19458

Cited by 114 publications

(137 citation statements)

References 29 publications

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“…Based on the obtained potential energy profiles at zero temperature, the characteristic barrier height V 0 of the TLS can be calculated by instanton theory 64 . Due to the heavy atoms involved, we can safely assume that for qualitative estimates, the instanton path is very similar to the calculated classical minimum energy path.…”

Section: Appendix D: Maximum Size Of Avoided Level Crossingmentioning

confidence: 99%

Identification of structural motifs as tunneling two-level systems in amorphous alumina at low temperatures

et al. 2014

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One of the most accepted models that describe the anomalous thermal behavior of amorphous materials at temperatures below 1 K relies on the quantum mechanical tunneling of atoms between two nearly equivalent potential energy wells forming a two-level system (TLS). Indirect evidence for TLSs is widely available. However, the atomistic structure of these TLSs remains an unsolved topic in the physics of amorphous materials. Here, using classical molecular dynamics, we found several hitherto unknown bistable structural motifs that may be key to understanding the anomalous thermal properties of amorphous alumina at low temperatures. We show through free energy profiles that the complex potential energy surface can be reduced to canonical TLSs. The predicted tunnel splittings from instanton theory, the number density, dipole moment, and coupling to external strain of the discovered motifs are consistent with experiments.

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Section: Appendix D: Maximum Size Of Avoided Level Crossingmentioning

confidence: 99%

Identification of structural motifs as tunneling two-level systems in amorphous alumina at low temperatures

et al. 2014

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“…Rather than computing the poles of E →G(a, −a, E), another systematic strategy to obtain one individual splitting [48] is to start with Herring's formula [25][26][27] that relies on the knowledge of the eigenfunctions outside the classically allowed regions in phase-space. Here, we will propose alternative formulae [28] that involve traces of a product of operators, among them the evolution operator,…”

Section: Tunnelling Splittingsmentioning

confidence: 99%

Instantons re-examined: Dynamical tunneling and resonant tunneling

Deunff

Mouchet²

2010

Phys. Rev. E

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Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instanton-like approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunnelling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunnelling or resonant tunnelling. Even though only onedimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunnelling.

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“…It also provides a platform for studying quantum tunneling between localized states in phase space. This problem is considerably different from the classical problem of tunneling in a symmetric double-well potential [29] (see also [30]). …”

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confidence: 99%

Time-translation-symmetry breaking in a driven oscillator: From the quantum coherent to the incoherent regime

et al. 2017

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We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. Such systems are intermediate between large closed systems and small dissipative systems, which both display the symmetry breaking, but have qualitatively different dynamics. As a nontrivial example we consider period tripling in a quantum nonlinear oscillator. We show that, for moderately strong driving, the period tripling is robust on an exponentially long time scale, which is further extended by an even weak decoherence.The breaking of translation symmetry in time, first proposed by Wilczek [1], has been attracting much attention recently. Such symmetry breaking can occur only away from thermal equilibrium [2]. It is of particular interest for periodically driven systems, which have a discrete time-translation symmetry imposed by the driving. Here, the time symmetry breaking is manifested in the onset of oscillations with a period that is a multiple of the driving period t F . Oscillations with period 2t F due to simultaneously initialized protected boundary states were studied in photonic quantum walks [3]; period-two oscillations can also be expected from the coexistence of Floquet Majorana fermions with quasienergies 0 and π/t F in a cold-atom system [4]. The onset of periodtwo phases was predicted and analyzed [5][6][7][8][9][10] in Floquet many-body localized systems, and the first observations of oscillations at multiples of the driving period in disordered systems were reported [11,12].In systems coupled to a thermal bath, on the other hand, the effect of period doubling has been well-known. A textbook example is a classical oscillator modulated close to twice its eigenfrequency and displaying vibrations with period 2t F [13]. The oscillator has two states of such vibrations; they have opposite phases, reminiscent of a ferromagnet with two orientations of the magnetization. Several aspects of the dynamics of a parametric oscillator in the quantum regime have been studied theoretically, cf. [14][15][16][17][18][19][20][21], and in experiments, cf. [22][23][24]. For a sufficiently strong driving field, a quantum dissipative oscillator, like a classical oscillator, mostly performs vibrations with period 2t F . The interplay of quantum fluctuations and dissipation leads to transitions between the period-two vibrational states, but the rate of these transitions is exponentially small [18].The goal of this paper is to study time symmetry breaking in isolated or almost isolated driven quantum systems with a few degrees of freedom. They are intermediate between large closed systems and dissipative systems, where the nature of the symmetry breaking is very different. To this end, we analyze a driven nonlinear quantum oscillator. Time symmetry breaking in this system should not be limited to period doubling. As an illustration of a behavior qualitatively different from period doubling, we consider period tripling and find the conditions where it occurs. We also address the role of decoherence and the co...

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Tunnel splittings for one-dimensional potential wells revisited

Cited by 114 publications

References 29 publications

Identification of structural motifs as tunneling two-level systems in amorphous alumina at low temperatures

Identification of structural motifs as tunneling two-level systems in amorphous alumina at low temperatures

Instantons re-examined: Dynamical tunneling and resonant tunneling

Time-translation-symmetry breaking in a driven oscillator: From the quantum coherent to the incoherent regime

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