Survey of the Hierarchical Equations of Motion in Tensor-Train format
for non-Markovian quantum dynamics
- URL: http://arxiv.org/abs/2303.04608v1
- Date: Wed, 8 Mar 2023 14:21:43 GMT
- Title: Survey of the Hierarchical Equations of Motion in Tensor-Train format
for non-Markovian quantum dynamics
- Authors: Etienne Mangaud, Amine Jaouadi, Alex Chin and Mich\`ele
Desouter-Lecomte
- Abstract summary: This work is a survey about the hierarchical equations of motion and their implementation with the tensor-train format.
We recall the link with the perturbative second order time convolution equations also known as the Bloch-Redfield equations.
The main points of the tensor-train expansion are illustrated in an example with a qubit interacting with a bath described by a Lorentzian spectral density.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This work is a pedagogical survey about the hierarchical equations of motion
and their implementation with the tensor-train format. These equations are a
great standard in non-perturbative non-Markovian open quantum systems. They are
exact for harmonic baths in the limit of relevant truncation of the hierarchy.
We recall the link with the perturbative second order time convolution
equations also known as the Bloch-Redfield equations. Some theoretical tools
characterizing non-Markovian dynamics such as the non- Markovianity measures or
the dynamical map are also briefly discussed in the context of HEOM
simulations. The main points of the tensor-train expansion are illustrated in
an example with a qubit interacting with a bath described by a Lorentzian
spectral density. Finally, we give three illustrative applications in which the
system-bath coupling operator is similar to that of the analytical treatment.
The first example revisits a model in which population-to-coherence transfer
via the bath creates a long-lasting coherence between two states. The second
one is devoted to the computation of stationary absorption and emission
spectra. We illustrate the link between the spectral density and the Stokes
shift in situations with and without nonadiabatic interaction. Finally, we
simulate an excitation transfer when the spectral density is discretized by
undamped modes to illustrate a situation in which the TT formulation is more
efficient than the standard one.
Related papers
- Semiclassical descriptions of dissipative dynamics of strongly interacting Bose gases in optical lattices [0.0]
We develop methods for describing real-time dynamics of dissipative Bose-Hubbard systems in a strongly interacting regime.
We numerically demonstrate that the discrete TWA approach is able to qualitatively capture the continuous quantum Zeno effect on dynamics.
arXiv Detail & Related papers (2023-07-30T08:39:06Z) - Exotic quantum liquids in Bose-Hubbard models with spatially-modulated
symmetries [0.0]
We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states.
We show that such systems feature a non-trivial Hilbert space fragmentation for momenta incommensurate with the lattice.
We conjecture that a Berezinskii-Kosterlitz-Thouless-type transition is driven by the unbinding of vortices along the temporal direction.
arXiv Detail & Related papers (2023-07-17T18:14:54Z) - Dual symplectic classical circuits: An exactly solvable model of
many-body chaos [0.0]
We prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones.
We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain.
arXiv Detail & Related papers (2023-07-04T15:48:41Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Geometric phase in a dissipative Jaynes-Cummings model: theoretical
explanation for resonance robustness [68.8204255655161]
We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models.
In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls.
We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
arXiv Detail & Related papers (2021-10-27T15:27:54Z) - Quantum coherence, correlations and nonclassical states in the two-qubit
Rabi model with parametric oscillator [0.0]
Quantum coherence and quantum correlations are studied in a strongly interacting system composed of two qubits and a parametric medium.
We employ the adiabatic approximation approach to analytically solve the system.
The reconstructed states are observed to be nearly pure generalized Bell states.
arXiv Detail & Related papers (2021-06-12T11:16:40Z) - From non-equilibrium Green's functions to quantum master equations for
the density matrix and out-of-time-order correlators: steady state and
adiabatic dynamics [0.0]
We consider a finite quantum system under slow driving and weakly coupled to thermal reservoirs at different temperatures.
We formulate the equations ruling the dynamics of these quantities by recourse to the Schwinger-Keldysh non-equilibrium Green's function formalism.
We illustrate the formalism in the case of a qutrit coupled to bosonic reservoirs and of a pair of interacting quantum dots attached to fermionic reservoirs.
arXiv Detail & Related papers (2021-03-07T15:15:22Z) - Dissipative flow equations [62.997667081978825]
We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations.
We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
arXiv Detail & Related papers (2020-07-23T14:47:17Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.