Reproducing Kernel Hilbert Space Approach to Non-Markovian Quantum Stochastic Models

• URL: http://arxiv.org/abs/2407.07231v1
• Date: Tue, 9 Jul 2024 21:10:54 GMT
• Title: Reproducing Kernel Hilbert Space Approach to Non-Markovian Quantum Stochastic Models
• Authors: John E. Gough, Haijin Ding, Nina H. Amini,
• Abstract summary: We give a derivation of the non-Markovian quantum state diffusion equation of Di'osi and Strunz. We show that the complex trajectories arises as a consequence of using the Bargmann-Segal representation of the bath.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give a derivation of the non-Markovian quantum state diffusion equation of Di{\'o}si and Strunz starting from a model of a quantum mechanical system coupled to a bosonic bath. We show that the complex trajectories arises as a consequence of using the Bargmann-Segal (complex wave) representation of the bath. In particular, we construct a reproducing kernel Hilbert space for the bath auto-correlation and realize the space of complex trajectories as a Hilbert subspace. The reproducing kernel naturally arises from a feature space where the underlying feature space is the one-particle Hilbert space of the bath quanta. We exploit this to derive the unravelling of the open quantum system dynamics and show equivalence to the equation of Di{\'o}si and Strunz. We also give an explicit expression for the reduced dynamics of a two-level system coupled to the bath via a Jaynes-Cummings interaction and show that this does indeed correspond to an exact solution of the Di{\'o}si-Strunz equation. Finally, we discuss the physical interpretation of the complex trajectories and show that they are intrinsically unobservable.

Related papers

• On the unraveling of open quantum dynamics [0.0]
  We show that the dynamics of an open quantum system generically admits an unraveling in the Hilbert space of the system. We derive the state-of-the-art form of the Di'osi-Gisin-Strunz random ostensible state equation in the context of a model problem.
  arXiv  Detail & Related papers  (2023-09-23T15:42:33Z)
• 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)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains [0.0]
  We show that the temporal decay of the autocorrelation in a disordered quantum spin chain is explicitly encoded in how the return probability on Hilbert space approaches its late-time saturation. Our treatment is rooted in an understanding of the morphology of the time-evolving state on the Hilbert-space graph, and corroborated by exact numerical results.
  arXiv  Detail & Related papers  (2023-05-10T18:00:02Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
  We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
  arXiv  Detail & Related papers  (2022-09-12T08:21:12Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole [0.0]
  We consider the problem of quantizing a particle on a 2-sphere. We construct the Hilbert space directly from the symmetry algebra. We show how the Casimir invariants of the algebra determine the bundle topology.
  arXiv  Detail & Related papers  (2020-11-10T04:42:08Z)
• Quantum Space, Quantum Time, and Relativistic Quantum Mechanics [0.0]
  We treat space and time as quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order translations Hamiltonian and momentum constraints.
  arXiv  Detail & Related papers  (2020-04-20T09:04:15Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

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.