Timing quantum particles from the perspective of Bohmian mechanics

1998 ◽  
Vol 23 (3-4) ◽  
pp. 795-807 ◽  
Author(s):  
C.R. Leavens
Keyword(s):  
Bohmian Mechanics ◽  
Quantum Particles

scholarly journals Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

scholarly journals Experimental nonlocal and surreal Bohmian trajectories

2016 ◽  
Vol 2 (2) ◽  
pp. e1501466 ◽  
Author(s):  
Dylan H. Mahler ◽  
Lee Rozema ◽  
Kent Fisher ◽  
Lydia Vermeyden ◽  
Kevin J. Resch ◽  
...  
Keyword(s):  
Bohmian Mechanics ◽  
Weak Measurement ◽  
Weak Measurements ◽  
Quantum Particles ◽  
Bohmian Trajectories

Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.

Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

scholarly journals Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

CORRELATION INTERACTIONS OF QUANTUM PARTICLES

2019 ◽  
Author(s):  
Evgeniy Krasnopevtsev
Keyword(s):  
Thermal State ◽  
Mutual Interference ◽  
Quantum Gas ◽  
Quantum Particles

Correlation of particles number in an equilibrium thermal state of quantum gas is caused mutual «interference repulsion» and antibunching at fermions and «interference attraction» and bunching at bosons.

Galileo Unbound

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Free Fall ◽  
The Sun ◽  
Quantum Field ◽  
Many Worlds ◽  
Quantum Particles ◽  
Light Rays ◽  
History Of ◽  
And Control ◽  
The Universe ◽  
Insight Into

Galileo Unbound: A Path Across Life, The Universe and Everything traces the journey that brought us from Galileo’s law of free fall to today’s geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman’s dilemma of quantum particles taking all paths at once—setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

Specific features of interference of photons and other quantum particles

2016 ◽  
Vol 71 (3) ◽  
pp. 258-265 ◽  
Author(s):  
A. V. Belinsky ◽  
V. B. Lapshin
Keyword(s):  
Quantum Particles
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