We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $Ψ=aΨ_{m_1,n_1}(x,y)+bΨ_{m_2,n_2}(x,y)+cΨ_{m_3,n_3}(x,y)$ . We first find the trajectories of the nodal points for different combinations of the quantum numbers $m,n$ . Then we study, in detail, a case with relatively large quantum numbers and two equal $m's$ . We find %We find first the nodal points where $Ψ=0$ . The nodes can be found analytically only if $m$ and $n$ are small. If two $m's$ (or two $n's$ are equal we can find explicitly the nodal points , which are of two types (1) fixed nodes independent of time and (2) moving nodes which from time to time collide with the fixed nodes and at particular times they go to infinity. Finally, we study the trajectories of quantum particles close to the nodal points and observe, for the first time, how chaos is generated in a complex system with multiple nodes scattered on the configuration space.We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $Ψ=aΨ_{m_1,n_1}(x,y)+bΨ_{m_2,n_2}(x,y)+cΨ_{m_3,n_3}(x,y)$. We first find the trajectories of the nodal points for different combinations of the quantum numbers $m,n$. Then we study, in detail, a case with relatively large quantum numbers and two equal $m's$. We find %We find first the nodal points where $Ψ=0$. The nodes can be found analytically only if $m$ and $n$ are small. If two $m's$ (or two $n's$ are equal we can find explicitly the nodal points , which are of two types (1) fixed nodes independent of time and (2) moving nodes which from time to time collide with the fixed nodes and at particular times they go to infinity. Finally, we study the trajectories of quantum particles close to the nodal points and observe, for the first time, how chaos is generated in a complex system with multiple nodes scattered on the configuration space.

arXiv:2205.11872May 24, 20220 citations

Space-time trajectories of quantum particles

Daniel C. Galehouse

International Journal of Theoretical PhysicsOct 1, 19813 citations

Creation rate of Dirac particles at a point source

Joscha Henheik, Roderich Tumulka

Abstract Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process ( Q t ) t ∈ R in the configuration space of a variable number of particles that is | ψ t | 2 -distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell’s jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).Abstract Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process ( Q t ) t ∈ R in the configuration space of a variable number of particles that is | ψ t | 2 -distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell’s jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).

arXiv:2211.16606Journal of Physics A Mathematical and TheoreticalSep 28, 20231 citation

Quantum Dynamics with Bohmian Trajectories

Dirk, André Deckert

Jan 1, 20080 citations

Bohmian trajectories and quantum phase space distributions

Nuno Costa Dias, João Nuno Prata

arXiv:quant-ph/0208156Physics Letters ASep 1, 200225 citations

We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form

Ψ=aΨ_{m_1,n_1}(x,y)+bΨ_{m_2,n_2}(x,y)+cΨ_{m_3,n_3}(x,y)

. We first find the trajectories of the nodal points for different combinations of the quantum numbers

m,n

. Then we study, in detail, a case with relatively large quantum numbers and two equal

m's

. We find %We find first the nodal points where

Ψ=0

. The nodes can be found analytically only if

m

and

n

are small. If two

m's

(or two

n's

are equal we can find explicitly the nodal points , which are of two types (1) fixed nodes independent of time and (2) moving nodes which from time to time collide with the fixed nodes and at particular times they go to infinity. Finally, we study the trajectories of quantum particles close to the nodal points and observe, for the first time, how chaos is generated in a complex system with multiple nodes scattered on the configuration space.