Tunneling in energy eigenstates and complex quantum trajectories

Mathew, Kiran; John, Moncy V.

doi:10.1007/s40509-015-0051-9

Cited by 4 publications

(6 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Yang [ 48 ] presented tunneling dynamics in the complex space, revealing a smooth trajectory which continuously connects the classical trajectory and tunneling trajectory. John [ 49 ] evaluated the reflection probability in terms of the reflected and incident complex trajectories.…”

Section: Introductionmentioning

confidence: 99%

Tunneling Quantum Dynamics in Ammonia

Yang

Han

2021

IJMS

View full text Add to dashboard Cite

Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

show abstract

Section: Introductionmentioning

confidence: 99%

Tunneling Quantum Dynamics in Ammonia

Yang

Han

2021

IJMS

View full text Add to dashboard Cite

show abstract

“…In [12], using the 'quantum trajectories' approach, we checked whether the coasting evolution of a universe that starts from singularity [4] will have exact quantum-classical correspondence and obtained a positive result. In that case, we have used the de Broglie-Bohm (dBB) [13,14] and modified de Broglie-Bohm (MdBB) [15][16][17][18][19][20] trajectory formulations of quantum mechanics. In the present paper, instead of writing the WD equation, we employ the operator method in canonical quantisation and show that the quantum cosmological wave function can be obtained as an exact solution to the corresponding wave equation for the universe.…”

Section: Introductionmentioning

confidence: 99%

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

John¹

2021

Int J Theor Phys

View full text Add to dashboard Cite

When the scale factor of expansion of the universe is written as a(t) ≡ Ae α (t) , with A as some real constant and α(t) a real function, the gravitational action I G appears in the same form as the matter action I M for a homogeneous and isotropic scalar field with a specific scale factor-dependent potential. We observe that by making analytic continuation of the Lagrangian function in this I G to the complex plane of α, one can obtain terms corresponding to both parts of a total action that describes a viable cosmological model. The solution gives a bouncing and coasting universe, which first contracts and then expands linearly, with a smooth bounce in between them. Such a bounce, called a Tolman wormhole, is due to a Casimir-like negative energy that appears naturally in the solution. In a novel approach to quantum cosmology, we perform canonical quantization of the above model using the operator method and show that it can circumvent the operator ordering ambiguity in the conventional formalism. It leads to a quantum wave equation for the universe, solving which we get the interesting result that the universe is in a ground state with nonzero energy. This solution is different from the Wheeler-DeWitt wave function and possesses exact quantum-classical correspondence during all epochs.

show abstract

“…It may be noted that dBB is not the only quantum trajectory formalism available in the literature. The Floyd, Faraggi and Matone (FFM) [10] and the modified de Broglie-Bohn (MdBB) [11,12,13,14,15] trajectory representations have also received wide attention in recent years. The equations of motion used in dBB and MdBB schemes are alike, of the general form mṙ i = ∇ i S, where S represents the Hamilton-Jacobi functions in the respective quantum Hamilton-Jacobi equations in the two schemes.…”

mentioning

confidence: 99%

“…But the MdBB quantum mechanics, which puts forward a new dynamics based on a complex action, is found successful in this case [11]. Similarly, in the tunneling of potential barriers, when the incident particle is described by a stationary energy eigenfunction, the dBB trajectories are always proceeding towards the potential barrier and there are no reflected trajectories [15]. The usual practice adopted in the dBB scheme to circumvent these is to take a wave packet as the initial wave function.…”

mentioning

confidence: 99%

“…But it may be noted that the continuity equation for Ψ ⋆ Ψ in real space is 'in-built' in the dBB scheme and hence for the wave-packets, it is only natural that the non-crossing trajectories evolve to a final distribution that coincides with the one predicted in standard quantum mechanics. On the other hand, in [15,18,19], it was shown that the crossing trajectories in the MdBB scheme (which also admits a continuity equation for |Ψ | 2 along the real space) can exhibit quantum tunneling through barriers, even for stationary states.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Interfering Quantum Trajectories Without Which-Way Information

Mathew¹,

John²

2017

Found Phys

Self Cite

View full text Add to dashboard Cite

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie-Bohm (dBB) and modified de Broglie-Bohm (MdBB) formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the 'which-way' information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie's wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results.

show abstract

Tunneling in energy eigenstates and complex quantum trajectories

Cited by 4 publications

References 35 publications

Tunneling Quantum Dynamics in Ammonia

Tunneling Quantum Dynamics in Ammonia

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

Interfering Quantum Trajectories Without Which-Way Information

Contact Info

Product

Resources

About