The Entropic Dynamics of Spin

• URL: http://arxiv.org/abs/2007.15719v2
• Date: Mon, 1 Feb 2021 11:59:07 GMT
• Title: The Entropic Dynamics of Spin
• Authors: Ariel Caticha and Nicholas Carrara
• Abstract summary: In Entropic Dynamics (ED) approach the essence of theory lies in its probabilistic nature while the Hilbert space structure plays a secondary and optional role. In this paper the ED framework is extended to describe a spin-1/2 point particle. The updating of all constraints is carried out in a way that stresses the central importance of symmetry principles.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the Entropic Dynamics (ED) approach the essence of quantum theory lies in its probabilistic nature while the Hilbert space structure plays a secondary and ultimately optional role. The dynamics of probability distributions is driven by the maximization of an entropy subject to constraints that carry the relevant physical information -- directionality, correlations, gauge interactions, etc. The challenge is to identify those constraints and to establish a criterion for how the constraints themselves are updated. In this paper the ED framework is extended to describe a spin-1/2 point particle. In ED spin is neither modelled as a rotating body, nor through the motion of a point particle; it is an epistemic property of the wave function. The constraint that reflects the peculiar rotational properties of spin is most effectively expressed in the language of geometric algebra. The updating of all constraints is carried out in a way that stresses the central importance of symmetry principles. First we identify the appropriate symplectic and metric structures in the phase space of probabilities, their conjugate momenta, and the spin variables. This construction yields a derivation of the Fubini-Study metric for a spin-1/2 particle which highlights its deep connection to information geometry. Then we construct an ED that preserves both the symplectic structure (a Hamiltonian flow) and the metric structure (a Killing flow). We show that generic Hamiltonian-Killing flows are linear in the wave function. Imposing further that the Hamiltonian be the generator of an entropic evolution in time leads to an entropic dynamics described by the Pauli equation. We conclude with a discussion of the new interpretation of the formalism which yields a physical picture that is significantly different from that provided by other interpretations.

Related papers

• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Entanglement of edge modes in (very) strongly correlated topological insulators [0.0]
  Quantum information theory is capable of identifying topological phases for a theory that exhibits quantum phase transition. We study entanglement entropy for a bi-layer SSH model, both in the presence and absence of Hubbard interaction. A remnant entropy survives in the non-trivial topological phase which is exactly due to the entanglement of the edge modes.
  arXiv  Detail & Related papers  (2023-12-21T06:04:04Z)
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review [19.372542786476803]
  A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath. In the steady state, we analyze the quantum counterpart of energy equipartition theorem. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
  arXiv  Detail & Related papers  (2023-06-05T07:59:35Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Dynamical detection of mean-field topological phases in an interacting Chern insulator [11.848843951626527]
  We propose a scheme based on quench dynamics to detect the mean-field topological phase diagram of an insulator. We find two characteristic times $t_s$ and $t_c$ which capture the emergence of dynamical self-consistent particle number density. The number of mean-field topological phase is determined by the spin polarizations of four Dirac points at the time $t_s$.
  arXiv  Detail & Related papers  (2022-06-22T12:37:15Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• $\mathcal{PT}$-symmetry in compact phase space for a linear Hamiltonian [0.0]
  We study the time evolution of a PT-symmetric, non-Hermitian quantum system for which the associated phase space is compact. We analyze how the non-Hermitian part of the Hamiltonian affects the time evolution of two archetypical quantum states, coherent and Dicke states.
  arXiv  Detail & Related papers  (2020-07-30T20:38:00Z)
• The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity [0.0]
  We propose a model for a quantum scalar field propagating in a dynamical space-time. Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.
  arXiv  Detail & Related papers  (2020-06-09T03:44:36Z)
• Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator [0.0]
  We study the consequences of a helicoidal geometry in the Schr"odinger equation dealing with an anisotropic mass tensor. We determine the eigenfunctions in terms of Confluent Heun Functions and compute the respective energy levels.
  arXiv  Detail & Related papers  (2020-05-03T23:47:11Z)
• 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.