Quantum wave representation of dissipative fluids

• URL: http://arxiv.org/abs/2308.05879v2
• Date: Tue, 2 Jan 2024 20:36:10 GMT
• Title: Quantum wave representation of dissipative fluids
• Authors: L. Salasnich, S. Succi, A. Tiribocchi
• Abstract summary: We present a mapping between a Schr"odinger equation with a shifted non-linear potential and the Navier-Stokes equation. The inclusion of the Bohm quantum potential plus the laplacian of the phase field in the non-linear term leads to continuity and momentum equations for a dissipative incompressible Navier-Stokes fluid.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a mapping between a Schr\"odinger equation with a shifted non-linear potential and the Navier-Stokes equation. Following a generalization of the Madelung transformations, we show that the inclusion of the Bohm quantum potential plus the laplacian of the phase field in the non-linear term leads to continuity and momentum equations for a dissipative incompressible Navier-Stokes fluid. An alternative solution, built using a complex quantum diffusion, is also discussed. The present models may capture dissipative effects in quantum fluids, such as Bose-Einstein condensates, as well as facilitate the formulation of quantum algorithms for classical dissipative fluids.

Related papers

• Quantum Particle Statistics in Classical Shallow Water Waves [4.995343972237369]
  We show that when locally oscillating particles are guided by real wave gradients, particles may exhibit trajectories of alternating periodic or chaotic dynamics. The particle probability distribution function of this analogy reveals the quantum statistics of the standard solutions of the Schr"odinger equation.
  arXiv  Detail & Related papers  (2024-09-29T09:40:19Z)
• Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation [33.76659022113328]
  This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension.
  arXiv  Detail & Related papers  (2024-07-22T03:52:14Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Quantum Simulation of Conical Intersections [7.85411031368342]
  We show how the conical intersections (CIs) can be correctly described on quantum devices. A hybrid quantum-classical procedure is used to locate the seam of CIs. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.
  arXiv  Detail & Related papers  (2024-01-28T04:14:43Z)
• Quantum mechanics without quantum potentials [0.0]
  Non-locality in quantum mechanics can be resolved by considering relativistically covariant diffusion in spacetime. We introduce the concept of momentum equilinear to replace the second-order Bohm-Newton equations of motion.
  arXiv  Detail & Related papers  (2024-01-08T18:51:38Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Quantum simulation of partial differential equations via Schrodingerisation [31.986350313948435]
  We present a simple new way to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations. This can be seen directly on the level of the dynamical equations without more sophisticated methods.
  arXiv  Detail & Related papers  (2022-12-28T17:32:38Z)
• A Potential Based Quantization Procedure of the Damped Oscillator [0.0]
  We formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned. We arrive at such an irreversible quantum theory by which the quantum losses can be described.
  arXiv  Detail & Related papers  (2022-04-06T15:17:03Z)
• Induced osmotic vorticity in the quantum hydrodynamical picture [0.0]
  Solution entails attenuation related effects as non-unitary evolution, non-exponential quantum decay and entropy production. Time-invariant equation for the probability density is derived, analogous to the tensor Lighthill equation in aeroacoustics.
  arXiv  Detail & Related papers  (2021-06-24T17:58:51Z)
• 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)
• 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)

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.