Describing the Wave Function Collapse Process with a State-dependent Hamiltonian

• URL: http://arxiv.org/abs/2301.09274v1
• Date: Mon, 23 Jan 2023 05:08:35 GMT
• Title: Describing the Wave Function Collapse Process with a State-dependent Hamiltonian
• Authors: Le Hu, Andrew N. Jordan
• Abstract summary: We show how the continuous collapse of the wave function can be described by the Schr"odinger equation with a time-dependent Hamiltonian. We then discuss how the above formalism can also be applied to describe the collapse of the wave function of mixed quantum states.
• Score: 3.8326963933937885
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is well-known that quantum mechanics admits two distinct evolutions: the unitary evolution, which is deterministic and well described by the Schr\"{o}dinger equation, and the collapse of the wave function, which is probablistic, generally non-unitary, and cannot be described by the Schr\"{o}dinger equation. In this paper, starting with pure states, we show how the continuous collapse of the wave function can be described by the Schr\"{o}dinger equation with a stochastic, time-dependent Hamiltonian. We analytically solve for the Hamiltonian responsible for projective measurements on an arbitrary $n$-level system and the position measurement on an harmonic oscillator in the ground state, and propose several experimental schemes to verify and utilize the conclusions. A critical feature is that the Hamiltonian must be state-dependent. We then discuss how the above formalism can also be applied to describe the collapse of the wave function of mixed quantum states. The formalism we proposed may unify the two distinct evolutions in quantum mechanics.

Related papers

• Contributions to the study of time dependent oscillators in Paul traps. Semiclassical approach [0.0]
  We investigate quantum dynamics for an ion confined within an oscillating quadrupole field. It is established that the Hamilton equations of motion, in both Schr"odinger and Heisenberg representations, are equivalent to the Hill equation. The quantum states for trapped ions are demonstrated to be Fock (number) states, while the exact solutions of the Schr"odinger equation for a trapped ion are exactly the quasienergy states.
  arXiv  Detail & Related papers  (2024-09-09T08:44:25Z)
• A non-Hermitian loop for a quantum measurement [0.0]
  We establish a framework for a mechanism steering state vector collapse through time evolution. For two-level systems, we put forward the phenomenon of chiral state conversion as a mechanism effectively eliminating superpositions.
  arXiv  Detail & Related papers  (2024-08-08T17:59:10Z)
• Wavefunction collapse driven by non-Hermitian disturbance [0.0]
  We model the interaction between a quantum particle and an "apparatus" through a non-Hermitian Hamiltonian term. We analyze how the strength and other parameters of the non-Hermitian perturbation influence the time-to-collapse of the wave function.
  arXiv  Detail & Related papers  (2024-04-25T09:25:17Z)
• 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)
• A model of wave function collapse in a quantum measurement of spin as the Schroedinger equation solution of a system with a simple harmonic oscillator in a bath [0.0]
  We present a set of exact system solutions to a model we developed to study wave function collapse in the quantum spin measurement process. Specifically, we calculated the wave function evolution for a simple harmonic oscillator of spin frac12, with its magnetic moment in interaction with a magnetic field.
  arXiv  Detail & Related papers  (2023-04-07T23:27:52Z)
• Emulating the measurement postulates of quantum mechanics via non-Hermitian Hamiltonian [0.0]
  We show that a non-Hermitian Hamiltonian operates during the process of measurement, which evolves any state to an attracting equilibrium state, thus, mimicking a "collapse" For a 2-level system, we also demonstrate that the dynamics generated by the Lindblad master equation can be replicated as an incoherent sum of the evolution by two separate non-Hermitian Hamiltonians.
  arXiv  Detail & Related papers  (2023-02-03T18:22:10Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• 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.