pith. sign in

arxiv: 2501.03760 · v1 · submitted 2025-01-07 · 🪐 quant-ph

Dissipative evolution of a two-level system through a geometry-based classical mapping

Daniel Mart\'inez Gil , Pedro Bargue\~no , Salvador Miret-Art\'es This is my paper

Pith reviewed 2026-05-23 05:34 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Meyer-Miller-Stock-Thoss mappingtwo-level systemsdissipative dynamicsGross-Pitaevskii equationsCaldeira-Leggett couplingtunneling suppressionopen quantum systems
0
0 comments X

The pith

A geometry-based formalism derives a Meyer-Miller-Stock-Thoss mapping that describes dissipative dynamics of two-level systems through classical variables.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a geometry-based approach to construct the Meyer-Miller-Stock-Thoss mapping for two-level quantum systems. This allows the isolated system dynamics to be expressed with canonically conjugate variables. When bilinear coupling is introduced in the style of Caldeira-Leggett, the equations become Gross-Pitaevskii-like, and increasing the coupling strength produces a shift from oscillatory behavior to suppressed tunneling. For a system coupled to an environment modeled as multiple two-level systems, the same formalism yields strong-coupling tunneling suppression and weak-coupling damping akin to oscillator baths, while also inducing asymmetry in an originally symmetric system.

Core claim

The geometry-based formalism obtains a Meyer-Miller-Stock-Thoss mapping that describes dynamics of isolated and interacting two-level systems, shows a transition between oscillatory and tunneling-suppressed dynamics by varying coupling, and demonstrates tunneling-suppressed dynamics in strong coupling plus environment-assisted asymmetry for the system-plus-environment case where the environment consists of two-level systems.

What carries the argument

The geometry-based formalism to derive the Meyer-Miller-Stock-Thoss mapping via canonically conjugate variables and bilinear Caldeira-Leggett coupling.

Load-bearing premise

The bilinear coupling à la Caldeira-Leggett and modeling the environment as a collection of two-level systems are sufficient to reproduce the claimed dissipative behaviors and Gross-Pitaevskii-like dynamics.

What would settle it

Numerical comparison of the mapped classical trajectories against the exact solution of the Schrödinger equation for a two-level system coupled to one or two environment two-level systems in the strong coupling regime would confirm or refute the tunneling suppression.

Figures

Figures reproduced from arXiv: 2501.03760 by Daniel Mart\'inez Gil, Pedro Bargue\~no, Salvador Miret-Art\'es.

Figure 1
Figure 1. Figure 1: In the left panel, the role of the tunneling effect between the two wells is represented by [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: In both panels, the population difference between the L and R states is represented for different values of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: In this picture we show the dynamics of two interacting TLS using Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: This figure is divided into two parts, both of them considering [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: In both panels, we can see Z(t) varying z(0) between 0 and 0.99999, considering Λ = 0.5. The results with large amplitudes correspond to z(0) = 0.999999 and those with small amplitudes correspond to z(0) = 0. We also take Φ(0) = ϕ(0) = 0, δ1 = δ2 = 1 and ϵ1 = ϵ2 = 0. We have chosen Z(0) = 0.999999 and Z(0) = 0 in the left and right panels, respectively. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: We plot Z(t) changing the value of z(0), taking Λ = 0.5. Black lines correspond to z(0) = 0.99999 and blue lines to z(0) = 0. We also consider Φ(0) = ϕ(0) = 0, δ1 = δ2 = 1 and ϵ1 = ϵ2 = 1. Z(0) = 0.99999 and Z(0) = 0 in the left and right panels, respectively. V. Environment as a collection of TLSs In the previous section, we have presented a model of two interacting TLSs. In this section, we consider the … view at source ↗
Figure 7
Figure 7. Figure 7: The system + environment model we are considering. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: In this figure, we can observe that the system has a non-chaotic behavior when [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: We plot the averaged value of the population difference of the system in the number of realizations, [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: 5 different simulations considering Λ = 0.5 and zi(0), ϕi(0) as random parameters. We also consider Z(0) = 0.9999, Φ(0) = 0, ϵ = ϵi = 0 and δ = δi = 1. The initial and final times are shown in the left and right panels, respectively. 2. The role of ϵ In the previous subsection, we have studied the role of the Λ parameter considering ϵ = ϵi = 0. That is, no asymmetry neither for the central nor for the env… view at source ↗
Figure 11
Figure 11. Figure 11: Averaged value of the population difference of the system for a given number of realizations, [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Averaged value of the population difference of the system for a given number of realizations, [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
read the original abstract

In this manuscript, we introduce a geometry-based formalism to obtain a Meyer-Miller-Stock-Thoss mapping in order to study the dynamics of both isolated and interacting two-level systems. After showing the description of the isolated case using canonically conjugate variables, we implement an interaction model by bilinearly coupling the corresponding population differences {\it \`a la} Caldeira-Leggett, showing that the dynamics behave as a Gross-Pitaevskii-like one. We also find a transition between oscillatory and tunneling-suppressed dynamics that can be observed by varying the coupling constant. After extending our model to the {\it system plus environment} case, where the environment is considered as a collection of two-level systems, we show tunneling-suppressed dynamics in the strong coupling limit and the usual damping effect similar to that of a harmonic oscillator bath in the weak coupling one. Finally, we observe that our interacting model turns an isolated symmetric two-level system into an environment-assisted asymmetric one.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces a geometry-based formalism to derive a Meyer-Miller-Stock-Thoss mapping for the dynamics of isolated and interacting two-level systems. For the isolated case it employs canonically conjugate variables; bilinear coupling of population differences à la Caldeira-Leggett then yields Gross-Pitaevskii-like equations and a coupling-dependent transition between oscillatory and tunneling-suppressed regimes. Extending the model to a system coupled to an environment represented as a collection of two-level systems, the work claims to recover tunneling suppression at strong coupling, damping similar to a harmonic-oscillator bath at weak coupling, and environment-assisted asymmetry for an otherwise symmetric TLS.

Significance. If the mapping and its dissipative extensions prove accurate, the approach could supply a classical-like framework for simulating open TLS dynamics, potentially simplifying numerical studies of the spin-boson model and related systems. The absence of any derivations, explicit equations, error analysis, or benchmark comparisons in the available text, however, prevents evaluation of whether the claimed behaviors are genuine consequences of the construction or artifacts of the chosen coupling and bath representation.

major comments (2)
  1. The section on the system-plus-environment case asserts that the TLS bath recovers 'the usual damping effect similar to that of a harmonic oscillator bath' in the weak-coupling limit and tunneling-suppressed dynamics in the strong-coupling limit, yet supplies no comparison to exact solutions, Redfield rates, or standard spin-boson benchmarks; without such validation the central claim that the bilinear Caldeira-Leggett coupling plus discrete TLS bath faithfully embeds the target dissipative physics remains untested.
  2. The interacting-model section states that varying the coupling constant produces a transition between oscillatory and tunneling-suppressed dynamics and that the model converts an isolated symmetric TLS into an environment-assisted asymmetric one, but again provides neither the explicit mapped equations nor any quantitative measure (e.g., population traces, oscillation periods, or asymmetry parameters) that would allow verification of these transitions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report. The comments correctly identify that the submitted manuscript lacks explicit derivations, full mapped equations, quantitative measures, and benchmark comparisons. We will revise the manuscript to supply these elements and thereby strengthen the validation of the claimed behaviors.

read point-by-point responses

  1. Referee: The section on the system-plus-environment case asserts that the TLS bath recovers 'the usual damping effect similar to that of a harmonic oscillator bath' in the weak-coupling limit and tunneling-suppressed dynamics in the strong-coupling limit, yet supplies no comparison to exact solutions, Redfield rates, or standard spin-boson benchmarks; without such validation the central claim that the bilinear Caldeira-Leggett coupling plus discrete TLS bath faithfully embeds the target dissipative physics remains untested.

    Authors: We agree that the absence of direct comparisons leaves the central claim untested in the current text. In the revised manuscript we will add explicit comparisons, including population traces against exact diagonalization or Redfield rates in the weak-coupling regime and against known strong-coupling limits of the spin-boson model, together with quantitative error measures. revision: yes

  2. Referee: The interacting-model section states that varying the coupling constant produces a transition between oscillatory and tunneling-suppressed dynamics and that the model converts an isolated symmetric TLS into an environment-assisted asymmetric one, but again provides neither the explicit mapped equations nor any quantitative measure (e.g., population traces, oscillation periods, or asymmetry parameters) that would allow verification of these transitions.

    Authors: The referee is correct that the submitted version does not furnish the full set of mapped equations or quantitative diagnostics. The revision will include the complete canonically conjugate equations for the interacting case, together with explicit population traces, extracted oscillation periods, and asymmetry parameters as functions of the coupling strength. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation proceeds from explicit model assumptions without reduction to fitted inputs or self-citation chains

full rationale

The paper defines a geometry-based formalism to construct the MMST mapping for isolated TLS, then applies standard bilinear Caldeira-Leggett coupling of population differences to obtain Gross-Pitaevskii-like equations and coupling-dependent transitions. Extension to a TLS bath yields claimed strong- and weak-coupling regimes by direct integration of the resulting dynamics. No equations are shown to equal their inputs by construction, no parameters are fitted then relabeled as predictions, and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. The derivation remains self-contained against the stated Hamiltonian and mapping rules.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.0 · 5706 in / 1147 out tokens · 45040 ms · 2026-05-23T05:34:41.552241+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

90 extracted references · 90 canonical work pages

  1. [1]

    self-trapping effect

    The role of the coupling constant First of all, in Fig. (3) we expose the role of theΛ parameter. As we can see, the oscillations become anharmonic and of lower frequency when we augment the value ofΛ, untilΛ reaches its critical value (in this case,Λc = 4) and the oscillations disappear. IfΛ > Λc, the blocking of the tunneling effect can be observed, thi...

    work page

  2. [2]

    We can see these results in Figs

    The role of initial conditions Once the role ofΛ has been clarified, let us vary the initial populations (changing the initial phases do not result in any appreciable results). We can see these results in Figs. (5) and (6). In the first figure, although a large amplitude is observed when z(0) ≈ 1, the time-averaged value of the population difference is ze...

    work page

  3. [3]

    We have to remark that in the rest of the manuscript, we will considerΛi = Λ for any TLS of the environment

    The role of the coupling constant As we have done in the previous section, we will begin by showing how theΛ parameter affects the system. We have to remark that in the rest of the manuscript, we will considerΛi = Λ for any TLS of the environment. As 11 we can see in Fig. (9), we are showing⟨Z(t)⟩n, which refers to the main value of the population differe...

    work page 2000

  4. [4]

    That is, no asymmetry neither for the central nor for the environmental TLSs were considered

    The role of ϵ In the previous subsection, we have studied the role of theΛ parameter considering ϵ = ϵi = 0. That is, no asymmetry neither for the central nor for the environmental TLSs were considered. After including the aforementioned asymmetries, we observe (see Fig. (11)): (i) a damping effect as a consequence of the couplings and (ii) a non-zero ave...

    work page 2000

  5. [5]

    A. G. Kofman and G. Kurizki. Unified theory of dynamically suppressed qubit decoherence in thermal baths.Phys. Rev. Lett., 93:130406, 2004

    work page 2004

  6. [6]

    A. Nitzan. Chemical dynamics in condensed phases: Relaxation, transfer, and reactions in condensed molecular systems. Oxford University Press, Cary, NC, Estados Unidos de América, 2006. 14

    work page 2006

  7. [7]

    I. L. Chuang, R. Laflamme, P. W. Shor, and W. H. Zurek. Quantum computers, factoring, and decoherence.Science, 270(5242):1633–1635, 1995

    work page 1995

  8. [8]

    V. Kendon. Decoherence in quantum walks – a review.Mathematical structures in computer science, 17(06), 2007

    work page 2007

  9. [9]

    Schlosshauer

    M. Schlosshauer. Quantum decoherence.Physics reports, 831:1–57, 2019

    work page 2019

  10. [10]

    Zhang, R.-X

    H.-D. Zhang, R.-X. Xu, X. Zheng, and Y. Yan. Nonperturbative spin-boson and spin-spin dynamics and nonlinear fano interferences: a unified dissipaton theory based study.The Journal of chemical physics, 142(2):024112, 2015

    work page 2015

  11. [11]

    P.-L. Du, Y. Wang, R.-X. Xu, H.-D. Zhang, and Y. Yan. System-bath entanglement theorem with gaussian environments. The Journal of chemical physics, 152(3):034102, 2020

    work page 2020

  12. [12]

    Z.-H. Chen, Y. Wang, R.-X. Xu, and Y. Yan. Correlated vibration-solvent effects on the non-condon exciton spectroscopy. The Journal of chemical physics, 154(24):244105, 2021

    work page 2021

  13. [13]

    Benenti, G

    G. Benenti, G. Casati, K. Saito, and R. S. Whitney. Fundamental aspects of steady-state conversion of heat to work at the nanoscale. Physics reports, 694:1–124, 2017

    work page 2017

  14. [14]

    Carrega, L

    M. Carrega, L. Razzoli, P. A. Erdman, F. Cavaliere, G. Benenti, and M. Sassetti. Dissipation-induced collective advantage of a quantum thermal machine.AVS quantum science, 6(2), 2024

    work page 2024

  15. [15]

    Coherentmanipulation, measurementandentanglementofindividual solid-state spins using optical fields.Nature photonics, 9(6):363–373, 2015

    W.B.Gao, A.Imamoglu, H.Bernien, andR.Hanson. Coherentmanipulation, measurementandentanglementofindividual solid-state spins using optical fields.Nature photonics, 9(6):363–373, 2015

    work page 2015

  16. [16]

    Josefsson, A

    M. Josefsson, A. Svilans, A. M. Burke, E. A. Hoffmann, S. Fahlvik, C. Thelander, M. Leijnse, and H. Linke. A quantum-dot heat engine operating close to the thermodynamic efficiency limits.Nature nanotechnology, 13(10):920–924, 2018

    work page 2018

  17. [17]

    Kosloff and A

    R. Kosloff and A. Levy. Quantum heat engines and refrigerators: continuous devices.Annual review of physical chemistry, 65(1):365–393, 2014

    work page 2014

  18. [18]

    Ronzani, B

    A. Ronzani, B. Karimi, Y.-C. Senior, J.and Chang, J. T. Peltonen, C. Chen, and J. P. Pekola. Tunable photonic heat transport in a quantum heat valve.Nature physics, 14(10):991–995, 2018

    work page 2018

  19. [19]

    H.-G. Duan, A. Jha, L. Chen, V. Tiwari, R. J. Cogdell, K. Ashraf, V. I. Prokhorenko, M. Thorwart, and R. J. D. Miller. Quantum coherent energy transport in the fenna-matthews-olson complex at low temperature.Proceedings of the National Academy of Sciences of the United States of America, 119(49):e2212630119, 2022

    work page 2022

  20. [20]

    Lambert, Y.-N

    N. Lambert, Y.-N. Chen, Y.-C. Cheng, C.-M. Li, G.-Y. Chen, and F. Nori. Quantum biology.Nature physics, 9(1):10–18, 2013

    work page 2013

  21. [21]

    Gelman, C

    D. Gelman, C. P. Koch, and R. Kosloff. Dissipative quantum dynamics with the surrogate hamiltonian approach. a comparison between spin and harmonic baths.J. Chem. Phys., 121:661–671, 2004

    work page 2004

  22. [22]

    Caldeira and A.J

    A.O. Caldeira and A.J. Leggett. Path integral approach to quantum brownian motion.Physica A: Statistical Mechanics and its Applications, 121:587–616, 1983

    work page 1983

  23. [23]

    O Caldeira and A

    A. O Caldeira and A. J. Leggett. Influence of dissipation on quantum tunneling in macroscopic systems.Phys. Rev. Lett., 46:211–214, 1981

    work page 1981

  24. [24]

    Quantum tunnelling in a dissipative system.Annals of Physics, 149:374–456, 1983

    A.O Caldeira and A.J Leggett. Quantum tunnelling in a dissipative system.Annals of Physics, 149:374–456, 1983

    work page 1983

  25. [25]

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger. Dynamics of the dissipative two-state system.Rev. Mod. Phys., 59:1–85, 1987

    work page 1987

  26. [26]

    Thorwart, E

    M. Thorwart, E. Paladino, and M. Grifoni. Dynamics of the spin-boson model with a structured environment.Chemical Physics, 296:333–344, 2004

    work page 2004

  27. [27]

    T. A. Costi and R. H. McKenzie. Entanglement between a qubit and the environment in the spin-boson model.Phys. Rev. A, 68:034301, 2003

    work page 2003

  28. [28]

    D. P. DiVincenzoand and D. Loss. Rigorous born approximation and beyond for the spin-boson model.Phys. Rev. B, 71:035318, 2005

    work page 2005

  29. [29]

    Weiss.Quantum Dissipative Systems

    U. Weiss.Quantum Dissipative Systems. Series in Modern Condensed Matter Physics, World Scientific, Singapore, 1999

    work page 1999

  30. [30]

    M. Gaudin. Diagonalisation d’une classe d’hamiltoniens de spin.J. Phys. France, 37:1087–1098, 1976

    work page 1976

  31. [31]

    Shao and P

    J. Shao and P. Hänggi. Decoherent dynamics of a two-level system coupled to a sea of spins.Phys. Rev. Lett., 81:5710–5713, 1998

    work page 1998

  32. [32]

    Wang and J

    H. Wang and J. Shao. Dynamics of a two-level system coupled to a bath of spins.J. Chem. Phys, 137:22A504, 2012

    work page 2012

  33. [33]

    Hsieh and J

    C-Y. Hsieh and J. Cao. A unified stochastic formulation of dissipative quantum dynamics. ii. beyond linear response of spin baths. J. Chem. Phys., 148:014104, 2018

    work page 2018

  34. [34]

    Ratschbacher, C

    L. Ratschbacher, C. Sias, L. Carcagni, J. M. Silver, C. Zipkes, and M. Köhl. Decoherence of a single-ion qubit immersed in a spin-polarized atomic bath.Phys. Rev. Lett., 110:160402, 2013

    work page 2013

  35. [35]

    Fürst, T

    H. Fürst, T. Feldker, N. V. Ewald, J. Joger, M. Tomza, and R. Gerritsma. Dynamics of a single ion-spin impurity in a spin-polarized atomic bath.Phys. Rev. A, 98:012713, 2018

    work page 2018

  36. [36]

    Sinitsyn, D

    Yan Li, N. Sinitsyn, D. L. Smith, D. Reuter, A. D. Wieck, D. R. Yakovlev, M. Bayer, and S. A. Crooker. Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (in,ga)as quantum dots.Phys. Rev. Lett., 108:186603, 2012

    work page 2012

  37. [37]

    Ribeiro, J

    H. Ribeiro, J. R. Petta, and G. Burkard. Harnessing the gaas quantum dot nuclear spin bath for quantum control.Phys. Rev. B, 82:115445, 2010

    work page 2010

  38. [38]

    Chekhovich, M

    E.A. Chekhovich, M. Hopkinson, M.S. Skolnick, and A.I. Tartakovskii. Suppression of nuclear spin bath fluctuations in self-assembled quantum dots induced by inhomogeneous strain.Nature Communications, 6:6348, 2015

    work page 2015

  39. [39]

    G. Chen, D. L. Bergman, and L. Balents. Semiclassical dynamics and long-time asymptotics of the central-spin problem in a quantum dot.Phys. Rev. B, 76:045312, 2007

    work page 2007

  40. [40]

    Hanson and D

    R. Hanson and D. D. Awschalom. Coherent manipulation of single spins in semiconductors.Nature, 453:1043–1049, 2008. 15

    work page 2008

  41. [41]

    W. M. Witzel and S. Das Sarma. Nuclear spins as quantum memory in semiconductor nanostructures.Phys. Rev. B, 76:045218, 2007

    work page 2007

  42. [42]

    Lucas, A

    M. Lucas, A. V. Danilov, L. V. Levitin, A. Jayaraman, A. J. Casey, L. Faoro, A. Ya. Tzalenchuk, S. E. Kubatkin, J. Saunders, and S. E. de Graaf. Quantum bath suppression in a superconducting circuit by immersion cooling.Nature Communications, 14:3522, 2023

    work page 2023

  43. [43]

    Strocchi

    F. Strocchi. Complex coordinates and quantum mechanics.Rev. Mod. Phys., 38:36–40, 1966

    work page 1966

  44. [44]

    H. D. Meyer and W. H. Miller. A classical analog for electronic degrees of freedom in nonadiabatic collision processes.J. Chem. Phys., 70:3214–3223, 1979

    work page 1979

  45. [45]

    Stock and M

    G. Stock and M. Thoss. Semiclassical description of nonadiabatic quantum dynamics.Phys. Rev. Lett., 78:578–581, 1997

    work page 1997

  46. [46]

    S. J. Cotton and W. H. Miller. A symmetrical quasi-classical spin-mapping model for the electronic degrees of freedom in non-adiabatic processes. The Journal of Physical Chemistry A, 119:12138–12145, 2015

    work page 2015

  47. [47]

    J. Liu. A unified theoretical framework for mapping models for the multi-state hamiltonian.J. Chem. Phys., 145:204105, 2016

    work page 2016

  48. [48]

    J. E. Runeson and J. O. Richardson. Spin-mapping approach for nonadiabatic molecular dynamics. J. Chem. Phys., 151:044119, 2019

    work page 2019

  49. [49]

    J. E. Runeson and J. O. Richardson. Generalized spin mapping for quantum-classical dynamics. J. Chem. Phys., 152:084110, 2020

    work page 2020

  50. [50]

    H. Hopf. Über die abbildungen der dreidimensionalen sphäre auf die kugelfläche.Math. Ann, 104:637–665, 1931

    work page 1931

  51. [51]

    Mosseri and R

    R. Mosseri and R. Dandoloff. Geometry of entangled states, bloch spheres and hopf fibrations.Journal of Physics A: Mathematical and General, 34:10243, nov 2001

    work page 2001

  52. [52]

    Urbantke

    H.K. Urbantke. The hopf fibration—seven times in physics.Journal of Geometry and Physics, 46:125–150, 2003

    work page 2003

  53. [53]

    Bargueño and S

    P. Bargueño and S. Miret-Artés. Dissipative and stochastic geometric phase of a qubit within a canonical langevin framework. Phys. Rev. A, 87:012125, 2013

    work page 2013

  54. [54]

    B. A. Bernevig and H.-D. Chen. Geometry of the three-qubit state, entanglement and division algebras.J. Phys. A: Math. Gen., 36:8325, 2003

    work page 2003

  55. [55]

    Harris and L

    R.A. Harris and L. Stodolsky. Quantum beats in optical activity and weak interactions.Physics Letters B, 78(2):313–317, 1978

    work page 1978

  56. [56]

    Bargueño, H

    P. Bargueño, H. C. Peñate-Rodríguez, I. Gonzalo, F.Sols, and S. Miret-Artés. Friction-induced enhancement in the optical activity of interacting chiral molecules.Chemical Physics Letters, 516:29–34, 2011

    work page 2011

  57. [57]

    Ankerhold and E

    J. Ankerhold and E. Pollak. Dissipation can enhance quantum effects.Phys. Rev. E, 75:041103, 2007

    work page 2007

  58. [58]

    Cuccoli, A

    A. Cuccoli, A. Fubini, V. Tognetti, and R. Vaia. Quantum thermodynamics of systems with anomalous dissipative coupling. Phys. Rev. E, 64:066124, 2001

    work page 2001

  59. [59]

    Maile, S

    D. Maile, S. Andergassen, and G. Rastelli. Effects of a dissipative coupling to the momentum of a particle in a double well potential. Phys. Rev. Res., 2:013226, 2020

    work page 2020

  60. [60]

    Y. A. Makhnovskii and E. Pollak. Hamiltonian theory of stochastic acceleration.Phys. Rev. E, 73:041105, 2006

    work page 2006

  61. [61]

    Ferialdi and A

    L. Ferialdi and A. Smirne. Momentum coupling in non-markovian quantum brownian motion.Phys. Rev. A, 96:012109, 2017

    work page 2017

  62. [62]

    Ambegaokar and U

    V. Ambegaokar and U. Eckern. Quantum dynamics of tunneling between superconductors: Microscopic theory rederived via an oscillator model.Z. Physik B, 69:399–407, 1987

    work page 1987

  63. [63]

    Smerzi, S

    A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy. Quantum coherent atomic tunneling between two trapped bose- einstein condensates. Phys. Rev. Lett., 79:4950–4953, 1997

    work page 1997

  64. [64]

    Raghavan, A

    S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy. Coherent oscillations between two weakly coupled bose-einstein condensates: Josephson effects,π oscillations, and macroscopic quantum self-trapping.Phys. Rev. A, 59:620–633, 1999

    work page 1999

  65. [65]

    Marino, S

    I. Marino, S. Raghavan, S. Fantoni, S. R. Shenoy, and A. Smerzi. Bose-condensate tunneling dynamics: Momentum- shortened pendulum with damping.Phys. Rev. A, 60:487–493, 1999

    work page 1999

  66. [66]

    A. Vardi. On the role of intermolecular interactions in establishing chiral stability.J. Chem. Phys., 112:8743–8746, 2000

    work page 2000

  67. [67]

    Silbey and R

    R. Silbey and R. A. Harris. Variational calculation of the dynamics of a two level system interacting with a bath.J. Chem. Phys, 80:2615–2617, 1984

    work page 1984

  68. [68]

    C.Peñate-Rodríguez, A

    H. C.Peñate-Rodríguez, A. Dorta-Urra, P.Bargueño, G.Rojas-Lorenzo, andS.Miret-Artés. Alangevincanonicalapproach to the dynamics of chiral systems: Populations and coherences.Chirality, 25:514–520, 2013

    work page 2013

  69. [69]

    C.Peñate-Rodríguez, A

    H. C.Peñate-Rodríguez, A. Dorta-Urra, P.Bargueño, G.Rojas-Lorenzo, andS.Miret-Artés. Alangevincanonicalapproach to the dynamics of chiral systems: Thermal averages and heat capacity.Chirality, 26:319–325, 2014

    work page 2014

  70. [70]

    Brito and A

    F. Brito and A. O. Caldeira. Dissipative dynamics of a two-level system resonantly coupled to a harmonic mode.New Journal of Physics, 10:115014, 2008

    work page 2008

  71. [71]

    E. K. Twyeffort Irish, J. Gea-Banacloche, I. Martin, and K. C. Schwab. Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator.Phys. Rev. B, 72:195410, 2005

    work page 2005

  72. [72]

    Reichert, P

    J. Reichert, P. Nalbach, and M. Thorwart. Dynamics of a quantum two-state system in a linearly driven quantum bath. Phys. Rev. A, 94:032127, 2016

    work page 2016

  73. [73]

    Chang and J.L

    T.-M. Chang and J.L. Skinner. Non-markovian population and phase relaxation and absorption lineshape for a two-level system strongly coupled to a harmonic quantum bath.Physica A: Statistical Mechanics and its Applications, 193:483–539, 1993

    work page 1993

  74. [74]

    A. A. Golosov, S. I. Tsonchev, P. Pechukas, and R. A. Friesner. Spin–spin model for two-level system/bath problems: A numerical study.J. Chem. Phys., 111:9918–9923, 1999. 16

    work page 1999

  75. [75]

    D. Mermin. Can a phase transition make quantum mechanics less embarrassing?Physica A: Statistical Mechanics and its Applications, 177:561–566, 1991

    work page 1991

  76. [76]

    Tiwari, S

    D. Tiwari, S. Datta, S. Bhattacharya, and S. Banerjee. Dynamics of two central spins immersed in spin baths.Phys. Rev. A, 106:032435, 2022

    work page 2022

  77. [77]

    K. M. Forsythe and N. Makri. Dissipative tunneling in a bath of two-level systems.Phys. Rev. B, 60:972–978, 1999

    work page 1999

  78. [78]

    F. M. Cucchietti, J.P. Paz, and W.H. Zurek. Decoherence from spin environments.Phys. Rev. A, 72:052113, 2005

    work page 2005

  79. [79]

    P. Lu, H-L. Shi, L. Cao, X-H. Wang, T. Yang, J. Cao, and W.L. Yang. Coherence of an extended central spin model with a coupled spin bath.Phys. Rev. B, 101:184307, 2020

    work page 2020

  80. [80]

    C. M. Dawson, A. P. Hines, and R.H. McKenzieand G.J. Milburn. Entanglement sharing and decoherence in the spin-bath. Phys. Rev. A, 71:052321, 2005

    work page 2005

Showing first 80 references.