Emulating the measurement postulates of quantum mechanics via non-Hermitian Hamiltonian

• URL: http://arxiv.org/abs/2302.01898v3
• Date: Tue, 15 Aug 2023 00:22:48 GMT
• Title: Emulating the measurement postulates of quantum mechanics via non-Hermitian Hamiltonian
• Authors: Gurpahul Singh, Ritesh K. Singh and Soumitro Banerjee (Indian Institute of Science Education and Research Kolkata)
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ever since the formulation of quantum mechanics, there is very little understanding of the process of the collapse of a wavefunction. We have proposed a dynamical model to emulate the measurement postulates of quantum mechanics. We postulate that a non-Hermitian Hamiltonian operates during the process of measurement, which evolves any state to an attracting equilibrium state, thus, mimicking a "collapse". We demonstrate this using a 2-level system and then extend it to an N-level system. 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.

Related papers

• 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)
• Magnetization in a non-equilibrium quantum spin system [0.0]
  We show that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.
  arXiv  Detail & Related papers  (2024-06-01T02:16:24Z)
• 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)
• Describing the Wave Function Collapse Process with a State-dependent Hamiltonian [3.8326963933937885]
  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.
  arXiv  Detail & Related papers  (2023-01-23T05:08:35Z)
• 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)
• Entanglement timescale and mixedness in non-Hermitian quantum systems [0.0]
  We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems. We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states. Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and $mathcalPT$-symmetric quantum field theory.
  arXiv  Detail & Related papers  (2022-09-23T15:53:07Z)
• 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)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• 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)

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.