quantum-computing

Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model

Hongfei Zhan, Ernest W.Z. Pan, and Zhenning Cai

26 min read

0 likes

⚡ Quantum Brief

AI Audio Summary

0:00 / 0:00

Click to play

Quantum News · Media Library

Understand this faster with AI

Ask ChatGPT

Research with Perplexity

Explain with Claude

Discuss on Grok

AbstractFocusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.Popular summaryQuantum systems are never completely isolated from their surroundings. Interactions with the environment lead to decoherence and energy dissipation, which pose key challenges for quantum technologies such as quantum computing, quantum communication, and nanoscale devices. The Caldeira-Leggett model is one of the most widely used theoretical frameworks for describing these open quantum systems. However, accurately simulating its real-time dynamics is computationally demanding because of both the high dimensionality of the system and the memory effects induced by the environment. Existing numerical approaches are therefore largely restricted to one-dimensional problems or systems with highly specialized structures. To overcome these challenges, we reduce the computational cost in two complementary ways. First, we exploit a low-rank approximation of the bath correlation function to reformulate the reduced density matrix into a representation resembling an ensemble of wavefunctions. Second, we employ the frozen Gaussian approximation, which describes quantum dynamics using Gaussian wavepackets whose centers approximate the particle motion. This provides an efficient representation of both the quantum evolution and the system-environment interaction. Consequently, the high-dimensional time integrations are reduced to only one- and two-dimensional integrals, independent of the order of the Dyson series expansion. To the best of our knowledge, this is the first deterministic algorithm capable of simulating the two-dimensional Caldeira-Leggett model. By substantially reducing both spatial and temporal complexity, our method paves the way for deterministic simulations of more realistic open systems and future numerical studies of multidimensional open quantum systems.► BibTeX data@article{Zhan2026reducingspatial, doi = {10.22331/q-2026-09-02-2201}, url = {https://doi.org/10.22331/q-2026-09-02-2201}, title = {Reducing {S}patial and {T}emporal {D}imensionality in the {M}ultidimensional {C}aldeira-{L}eggett {M}odel}, author = {Zhan, Hongfei and Pan, Ernest W.Z. and Cai, Zhenning}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2201}, month = sep, year = {2026} }► References [1] M Grigorescu. ``Decoherence and dissipation in quantum two-state systems''. Physica A: Statistical Mechanics and its Applications 256, 149–162 (1998). https://doi.org/10.1016/S0378-4371(98)00076-4 [2] Maximilian Schlosshauer. ``Quantum decoherence''. Physics Reports 831, 1–57 (2019). https://doi.org/10.1016/j.physrep.2019.10.001 [3] Emanuel Knill and Raymond Laflamme. ``Theory of quantum error-correcting codes''. Physical Review A 55, 900 (1997). https://doi.org/10.1103/PhysRevA.55.900 [4] Michael A Nielsen and Isaac L Chuang. ``Quantum computation and quantum information''. Cambridge university press. (2010). https://doi.org/10.1017/CBO9780511976667 [5] Heinz-Peter Breuer and Francesco Petruccione. ``The theory of open quantum systems''. OUP Oxford. (2002). https://doi.org/10.1093/acprof:oso/9780199213900.001.0001 [6] Amir O Caldeira and Anthony J Leggett. ``Path integral approach to quantum brownian motion''. Physica A: Statistical mechanics and its Applications 121, 587–616 (1983). https://doi.org/10.1016/0378-4371(83)90013-4 [7] David Chandler and Jerome K Percus. ``Introduction to modern statistical mechanics'' (1988). [8] Nancy Makri. ``The linear response approximation and its lowest order corrections: An influence functional approach''. The Journal of Physical Chemistry B 103, 2823–2829 (1999). https://doi.org/10.1021/jp9847540 [9] Sudip Chakravarty and Anthony J Leggett. ``Dynamics of the two-state system with ohmic dissipation''. Physical review letters 52, 5 (1984). https://doi.org/10.1103/PhysRevLett.52.5 [10] Michael Thorwart, Elisabetta Paladino, and Milena Grifoni. ``Dynamics of the spin-boson model with a structured environment''. Chemical Physics 296, 333–344 (2004). https://doi.org/10.1016/j.chemphys.2003.10.007 [11] Meng Xu and Joachim Ankerhold. ``About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach''.

The European Physical Journal Special Topics 232, 3209–3217 (2023). https://doi.org/10.1140/epjs/s11734-023-01000-6 [12] Nancy Makri. ``Modular path integral methodology for real-time quantum dynamics''. The Journal of Chemical Physics 149 (2018). https://doi.org/10.1063/1.5058223 [13] Geshuo Wang and Zhenning Cai. ``Real-time simulation of open quantum spin chains with the inchworm method''. Journal of Chemical Theory and Computation 19, 8523–8540 (2023). https://doi.org/10.1021/acs.jctc.3c00751 [14] Yixiao Sun, Geshuo Wang, and Zhenning Cai. ``Simulation of spin chains with off-diagonal coupling using the inchworm method''. Journal of Chemical Theory and Computation 20, 9321–9338 (2024). https://doi.org/10.1021/acs.jctc.4c00864 [15] Yaming Yan, Meng Xu, Tianchu Li, and Qiang Shi. ``Efficient propagation of the hierarchical equations of motion using the tucker and hierarchical tucker tensors''. The Journal of Chemical Physics 154 (2021). https://doi.org/10.1063/5.0050720 [16] A Erpenbeck, W-T Lin, T Blommel, L Zhang, S Iskakov, L Bernheimer, Y Núñez-Fernández, G Cohen, O Parcollet, X Waintal, et al. ``Tensor train continuous time solver for quantum impurity models''. Physical Review B 107, 245135 (2023). https://doi.org/10.1103/PhysRevB.107.245135 [17] Amir O Caldeira and Anthony J Leggett. ``Influence of dissipation on quantum tunneling in macroscopic systems''. Physical review letters 46, 211 (1981). https://doi.org/10.1103/PhysRevLett.46.211 [18] AO Caldeira and Anthony J Leggett. ``Influence of damping on quantum interference: An exactly soluble model''. Physical Review A 31, 1059 (1985). https://doi.org/10.1103/PhysRevA.31.1059 [19] Geshuo Wang, Siyao Yang, and Zhenning Cai. ``Solving caldeira-leggett model by inchworm method with frozen gaussian approximation''. Quantum 9, 1667 (2025). https://doi.org/10.22331/q-2025-03-24-1667 [20] Sadao Nakajima. ``On quantum theory of transport phenomena: Steady diffusion''. Progress of Theoretical Physics 20, 948–959 (1958). https://doi.org/10.1143/PTP.20.948 [21] Robert Zwanzig. ``Ensemble method in the theory of irreversibility''. The Journal of Chemical Physics 33, 1338–1341 (1960). https://doi.org/10.1063/1.1731409 [22] Qiang Shi and Eitan Geva. ``A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling''. The Journal of chemical physics 119, 12063–12076 (2003). https://doi.org/10.1063/1.1624830 [23] Ming-Liang Zhang, Being J Ka, and Eitan Geva. ``Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation''. The Journal of chemical physics 125 (2006). https://doi.org/10.1063/1.2218342 [24] Guy Cohen and Eran Rabani. ``Memory effects in nonequilibrium quantum impurity models''. Physical Review B—Condensed Matter and Materials Physics 84, 075150 (2011). https://doi.org/10.1103/PhysRevB.84.075150 [25] Guy Cohen, Emanuel Gull, David R Reichman, Andrew J Millis, and Eran Rabani. ``Numerically exact long-time magnetization dynamics at the nonequilibrium kondo crossover of the anderson impurity model''. Physical Review B—Condensed Matter and Materials Physics 87, 195108 (2013). https://doi.org/10.1103/PhysRevB.87.195108 [26] Eli Y Wilner, Haobin Wang, Guy Cohen, Michael Thoss, and Eran Rabani. ``Bistability in a nonequilibrium quantum system with electron-phonon interactions''. Physical Review B—Condensed Matter and Materials Physics 88, 045137 (2013). https://doi.org/10.1103/PhysRevB.88.045137 [27] Aaron Kelly and Thomas E Markland. ``Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics''. The Journal of chemical physics 139 (2013). https://doi.org/10.1063/1.4812355 [28] Aaron Kelly, Andrés Montoya-Castillo, Lu Wang, and Thomas E Markland. ``Generalized quantum master equations in and out of equilibrium: When can one win?''. The Journal of chemical physics 144 (2016). https://doi.org/10.1063/1.4948612 [29] Goran Lindblad. ``On the generators of quantum dynamical semigroups''. Communications in mathematical physics 48, 119–130 (1976). https://doi.org/10.1007/BF01608499 [30] Javier Cerrillo and Jianshu Cao. ``Non-markovian dynamical maps: numerical processing of open quantum trajectories''. Physical review letters 112, 110401 (2014). https://doi.org/10.1103/PhysRevLett.112.110401 [31] Robert Rosenbach, Javier Cerrillo, Susana F Huelga, Jianshu Cao, and Martin B Plenio. ``Efficient simulation of non-markovian system-environment interaction''. New Journal of Physics 18, 023035 (2016). https://doi.org/10.1088/1367-2630/18/2/023035 [32] Yoshitaka Tanimura. ``Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath''. Physical Review A 41, 6676 (1990). https://doi.org/10.1103/PhysRevA.41.6676 [33] Yoshitaka Tanimura and Ryogo Kubo. ``Time evolution of a quantum system in contact with a nearly gaussian-markoffian noise bath''. Journal of the Physical Society of Japan 58, 101–114 (1989). https://doi.org/10.1143/JPSJ.58.101 [34] Yoshitaka Tanimura. ``Numerically ``exact'' approach to open quantum dynamics: The hierarchical equations of motion (heom)''. The Journal of chemical physics 153 (2020). https://doi.org/10.1063/5.0011599 [35] Aidan Strathearn, Peter Kirton, Dainius Kilda, Jonathan Keeling, and Brendon William Lovett. ``Efficient non-markovian quantum dynamics using time-evolving matrix product operators''. Nature communications 9, 3322 (2018). https://doi.org/10.1038/s41467-018-05617-3 [36] Moritz Cygorek, Michael Cosacchi, Alexei Vagov, Vollrath Martin Axt, Brendon W Lovett, Jonathan Keeling, and Erik M Gauger. ``Simulation of open quantum systems by automated compression of arbitrary environments''. Nature Physics 18, 662–668 (2022). https://doi.org/10.1038/s41567-022-01544-9 [37] Dominic Gribben, Dominic M Rouse, Jake Iles-Smith, Aidan Strathearn, Henry Maguire, Peter Kirton, Ahsan Nazir, Erik M Gauger, and Brendon W Lovett. ``Exact dynamics of nonadditive environments in non-markovian open quantum systems''. PRX Quantum 3, 010321 (2022). https://doi.org/10.1103/PRXQuantum.3.010321 [38] Yuriel Núñez Fernández, Matthieu Jeannin, Philipp T Dumitrescu, Thomas Kloss, Jason Kaye, Olivier Parcollet, and Xavier Waintal. ``Learning feynman diagrams with tensor trains''. Physical Review X 12, 041018 (2022). https://doi.org/10.1103/PhysRevX.12.041018 [39] Nathan Ng, Gunhee Park, Andrew J Millis, Garnet Kin-Lic Chan, and David R Reichman. ``Real-time evolution of anderson impurity models via tensor network influence functionals''. Physical Review B 107, 125103 (2023). https://doi.org/10.1103/PhysRevB.107.125103 [40] Julian Thoenniss, Michael Sonner, Alessio Lerose, and Dmitry A Abanin. ``Efficient method for quantum impurity problems out of equilibrium''. Physical Review B 107, L201115 (2023). https://doi.org/10.1103/PhysRevB.107.L201115 [41] Mithilesh Nayak, Julian Thoenniss, Michael Sonner, Dmitry A Abanin, and Philipp Werner. ``Steady-state dynamical mean field theory based on influence functional matrix product states''. Physical Review B 112, 035103 (2025). https://doi.org/10.1103/xsbn-jk16 [42] Richard Phillips Feynman. ``Space-time approach to non-relativistic quantum mechanics''. Reviews of modern physics 20, 367 (1948). https://doi.org/10.1103/RevModPhys.20.367 [43] RP Feynman, AR Hibbs, and George H Weiss. ``Quantum mechanics and path integrals''. Physics Today 19, 89–89 (1966). [44] S Weiss, J Eckel, M Thorwart, and R Egger. ``Iterative real-time path integral approach to nonequilibrium quantum transport''. Physical Review B—Condensed Matter and Materials Physics 77, 195316 (2008). https://doi.org/10.1103/PhysRevB.77.195316 [45] Dvira Segal, Andrew J Millis, and David R Reichman. ``Numerically exact path-integral simulation of nonequilibrium quantum transport and dissipation''. Physical Review B—Condensed Matter and Materials Physics 82, 205323 (2010). https://doi.org/10.1103/PhysRevB.82.205323 [46] Lena Simine and Dvira Segal. ``Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions''. The Journal of Chemical Physics 138 (2013). https://doi.org/10.1063/1.4808108 [47] Nancy Makri. ``Improved feynman propagators on a grid and non-adiabatic corrections within the path integral framework''. Chemical physics letters 193, 435–445 (1992). https://doi.org/10.1016/0009-2614(92)85654-S [48] Richard Phillips Feynman and Frank L Vernon Jr. ``The theory of a general quantum system interacting with a linear dissipative system''. Annals of physics 24, 118–173 (1963). https://doi.org/10.1016/0003-4916(63)90068-X [49] Nancy Makri. ``Numerical path integral techniques for long time dynamics of quantum dissipative systems''. Journal of Mathematical Physics 36, 2430–2457 (1995). https://doi.org/10.1063/1.531046 [50] Nancy Makri. ``Quantum dissipative dynamics: A numerically exact methodology''. The Journal of Physical Chemistry A 102, 4414–4427 (1998). https://doi.org/10.1021/jp980359y [51] Nancy Makri. ``Blip decomposition of the path integral: Exponential acceleration of real-time calculations on quantum dissipative systems''. The Journal of chemical physics 141 (2014). https://doi.org/10.1063/1.4896736 [52] Nancy Makri. ``Blip-summed quantum–classical path integral with cumulative quantum memory''. Faraday discussions 195, 81–92 (2016). https://doi.org/10.1039/C6FD00142D [53] Geshuo Wang and Zhenning Cai. ``Differential equation based path integral for open quantum systems''. SIAM Journal on Scientific Computing 44, B771–B804 (2022). https://doi.org/10.1137/21M1439833 [54] Nancy Makri. ``Kink sum for long-memory small matrix path integral dynamics''. The Journal of Physical Chemistry B 128, 2469–2480 (2024). https://doi.org/10.1021/acs.jpcb.3c08282 [55] Nancy Makri. ``Small matrix path integral for system-bath dynamics''. Journal of Chemical Theory and Computation 16, 4038–4049 (2020). https://doi.org/10.1021/acs.jctc.0c00039 [56] Nancy Makri. ``Small matrix path integral with extended memory''. Journal of Chemical Theory and Computation 17, 1–6 (2020). https://doi.org/10.1021/acs.jctc.0c00987 [57] Nancy Makri. ``Small matrix disentanglement of the path integral: overcoming the exponential tensor scaling with memory length''. The Journal of Chemical Physics 152 (2020). https://doi.org/10.1063/1.5139473 [58] Geshuo Wang and Zhenning Cai. ``Tree-based implementation of the small matrix path integral for system-bath dynamics''. Communications in Computational Physics 36, 389–418 (2024). https://doi.org/10.4208/cicp.OA-2023-0329 [59] Nikolai V Prokof'ev and Boris V Svistunov. ``Polaron problem by diagrammatic quantum monte carlo''. Physical review letters 81, 2514 (1998). https://doi.org/10.1103/PhysRevLett.81.2514 [60] Philipp Werner, Takashi Oka, and Andrew J Millis. ``Diagrammatic monte carlo simulation of nonequilibrium systems''. Physical Review B—Condensed Matter and Materials Physics 79, 035320 (2009). https://doi.org/10.1103/PhysRevB.79.035320 [61] EY Loh Jr, JE Gubernatis, RT Scalettar, SR White, DJ Scalapino, and RL Sugar. ``Sign problem in the numerical simulation of many-electron systems''. Physical Review B 41, 9301 (1990). https://doi.org/10.1103/PhysRevB.41.9301 [62] Zhenning Cai, Jianfeng Lu, and Siyao Yang. ``Numerical analysis for inchworm monte carlo method: Sign problem and error growth''. Mathematics of Computation 92, 1141–1209 (2023). https://doi.org/10.1090/mcom/3785 [63] Nikolay Prokof’ev and Boris Svistunov. ``Bold diagrammatic monte carlo technique: When the sign problem is welcome''. Physical review letters 99, 250201 (2007). https://doi.org/10.1103/PhysRevLett.99.250201 [64] NV Prokof’ev and BV Svistunov. ``Bold diagrammatic monte carlo: A generic sign-problem tolerant technique for polaron models and possibly interacting many-body problems''. Physical Review B—Condensed Matter and Materials Physics 77, 125101 (2008). https://doi.org/10.1103/PhysRevB.77.125101 [65] Hsing-Ta Chen, Guy Cohen, and David R Reichman. ``Inchworm monte carlo for exact non-adiabatic dynamics. i. theory and algorithms''. The Journal of chemical physics 146 (2017). https://doi.org/10.1063/1.4974328 [66] Zhenning Cai, Jianfeng Lu, and Siyao Yang. ``Inchworm monte carlo method for open quantum systems''. Communications on Pure and Applied Mathematics 73, 2430–2472 (2020). https://doi.org/10.1002/cpa.21888 [67] Aviel Boag, Emanuel Gull, and Guy Cohen. ``Inclusion-exclusion principle for many-body diagrammatics''. Physical Review B 98, 115152 (2018). https://doi.org/10.1103/PhysRevB.98.115152 [68] Siyao Yang, Zhenning Cai, and Jianfeng Lu. ``Inclusion–exclusion principle for open quantum systems with bosonic bath''. New Journal of Physics 23, 063049 (2021). https://doi.org/10.1088/1367-2630/ac02e1 [69] Zhenning Cai, Geshuo Wang, and Siyao Yang. ``The bold-thin-bold diagrammatic monte carlo method for open quantum systems''. SIAM Journal on Scientific Computing 45, A1812–A1843 (2023). https://doi.org/10.1137/22M1499297 [70] Gian-Carlo Wick. ``The evaluation of the collision matrix''. Physical review 80, 268 (1950). https://doi.org/10.1103/PhysRev.80.268 [71] Leonid V Keldysh. ``Diagram technique for nonequilibrium processes''.

In Selected Papers of Leonid V Keldysh. Pages 47–55. World Scientific (2024). [72] Lajos Diósi and Walter T Strunz. ``The non-markovian stochastic schrödinger equation for open systems''. Physics Letters A 235, 569–573 (1997). https://doi.org/10.1016/S0375-9601(97)00717-2 [73] Lajos Diósi, Nicolas Gisin, and Walter T Strunz. ``Non-markovian quantum state diffusion''. Physical Review A 58, 1699 (1998). https://doi.org/10.1103/PhysRevA.58.1699 [74] Dieter Suess, Alexander Eisfeld, and Walter T Strunz. ``Hierarchy of stochastic pure states for open quantum system dynamics''. Physical review letters 113, 150403 (2014). https://doi.org/10.1103/PhysRevLett.113.150403 [75] Sohang Kundu and Nancy Makri. ``Modular path integral for finite-temperature dynamics of extended systems with intramolecular vibrations''. The Journal of Chemical Physics 153 (2020). https://doi.org/10.1063/5.0014838 [76] Nancy Makri. ``Two-tier modular anharmonic small matrix path integral with composite spin-boson baths''. Journal of Chemical Theory and Computation 20, 8405–8411 (2024). https://doi.org/10.1021/acs.jctc.4c00980 [77] Eric J Heller. ``Frozen gaussians: A very simple semiclassical approximation''. Journal of Chemical Physics 75, 2923–2931 (1981). https://doi.org/10.1063/1.442382 [78] Jianfeng Lu and Xu Yang. ``Frozen gaussian approximation for high frequency wave propagation''. Communications in Mathematical Sciences 9, 663––683 (2011). https://doi.org/10.4310/CMS.2011.v9.n3.a2 [79] Kaizhao Liu and Jianfeng Lu. ``Error bounds for open quantum systems with harmonic bosonic bath''. Quantum 9, 1896 (2025). https://doi.org/10.22331/q-2025-10-28-1896 [80] Jason Kaye, Kun Chen, and Olivier Parcollet. ``Discrete lehmann representation of imaginary time green's functions''. Physical Review B 105, 235115 (2022). https://doi.org/10.1103/PhysRevB.105.235115 [81] Dominik Kiese, Hugo UR Strand, Kun Chen, Nils Wentzell, Olivier Parcollet, and Jason Kaye. ``Discrete lehmann representation of three-point functions''. Physical Review B 111, 035135 (2025). https://doi.org/10.1103/PhysRevB.111.035135Cited byCould not fetch Crossref cited-by data during last attempt 2026-09-02 10:36:59: Could not fetch cited-by data for 10.22331/q-2026-09-02-2201 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-09-02 10:36:59: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractFocusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.Popular summaryQuantum systems are never completely isolated from their surroundings. Interactions with the environment lead to decoherence and energy dissipation, which pose key challenges for quantum technologies such as quantum computing, quantum communication, and nanoscale devices. The Caldeira-Leggett model is one of the most widely used theoretical frameworks for describing these open quantum systems. However, accurately simulating its real-time dynamics is computationally demanding because of both the high dimensionality of the system and the memory effects induced by the environment. Existing numerical approaches are therefore largely restricted to one-dimensional problems or systems with highly specialized structures. To overcome these challenges, we reduce the computational cost in two complementary ways. First, we exploit a low-rank approximation of the bath correlation function to reformulate the reduced density matrix into a representation resembling an ensemble of wavefunctions. Second, we employ the frozen Gaussian approximation, which describes quantum dynamics using Gaussian wavepackets whose centers approximate the particle motion. This provides an efficient representation of both the quantum evolution and the system-environment interaction. Consequently, the high-dimensional time integrations are reduced to only one- and two-dimensional integrals, independent of the order of the Dyson series expansion. To the best of our knowledge, this is the first deterministic algorithm capable of simulating the two-dimensional Caldeira-Leggett model. By substantially reducing both spatial and temporal complexity, our method paves the way for deterministic simulations of more realistic open systems and future numerical studies of multidimensional open quantum systems.► BibTeX data@article{Zhan2026reducingspatial, doi = {10.22331/q-2026-09-02-2201}, url = {https://doi.org/10.22331/q-2026-09-02-2201}, title = {Reducing {S}patial and {T}emporal {D}imensionality in the {M}ultidimensional {C}aldeira-{L}eggett {M}odel}, author = {Zhan, Hongfei and Pan, Ernest W.Z. and Cai, Zhenning}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2201}, month = sep, year = {2026} }► References [1] M Grigorescu. ``Decoherence and dissipation in quantum two-state systems''. Physica A: Statistical Mechanics and its Applications 256, 149–162 (1998). https://doi.org/10.1016/S0378-4371(98)00076-4 [2] Maximilian Schlosshauer. ``Quantum decoherence''. Physics Reports 831, 1–57 (2019). https://doi.org/10.1016/j.physrep.2019.10.001 [3] Emanuel Knill and Raymond Laflamme. ``Theory of quantum error-correcting codes''. Physical Review A 55, 900 (1997). https://doi.org/10.1103/PhysRevA.55.900 [4] Michael A Nielsen and Isaac L Chuang. ``Quantum computation and quantum information''. Cambridge university press. (2010). https://doi.org/10.1017/CBO9780511976667 [5] Heinz-Peter Breuer and Francesco Petruccione. ``The theory of open quantum systems''. OUP Oxford. (2002). https://doi.org/10.1093/acprof:oso/9780199213900.001.0001 [6] Amir O Caldeira and Anthony J Leggett. ``Path integral approach to quantum brownian motion''. Physica A: Statistical mechanics and its Applications 121, 587–616 (1983). https://doi.org/10.1016/0378-4371(83)90013-4 [7] David Chandler and Jerome K Percus. ``Introduction to modern statistical mechanics'' (1988). [8] Nancy Makri. ``The linear response approximation and its lowest order corrections: An influence functional approach''. The Journal of Physical Chemistry B 103, 2823–2829 (1999). https://doi.org/10.1021/jp9847540 [9] Sudip Chakravarty and Anthony J Leggett. ``Dynamics of the two-state system with ohmic dissipation''. Physical review letters 52, 5 (1984). https://doi.org/10.1103/PhysRevLett.52.5 [10] Michael Thorwart, Elisabetta Paladino, and Milena Grifoni. ``Dynamics of the spin-boson model with a structured environment''. Chemical Physics 296, 333–344 (2004). https://doi.org/10.1016/j.chemphys.2003.10.007 [11] Meng Xu and Joachim Ankerhold. ``About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach''.

Read Original

Source Information

Source: Quantum Science and Technology (arXiv overlay)

Website: https://quantum-journal.org/feed

Discussion

0 professional contributions

Be the first to add a constructive contribution.

Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model

Tags

Source Information