Geometric description of Schrödinger equation in Finsler and Funk geometry

Bashir, Asma; Koch, Benjamin; Wasay, Muhammad Abdul

doi:10.1142/s0219887819500981

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…[8], and a different approach to find geometric duality for quantum equations in the pilot-wave limit was presented in Refs. [9][10][11]. Studies on Dirac approach for particle constrained on a helicoid and for a free particle on S 3 were carried out in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

et al. 2022

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The classical and quantum dynamics of particles constrained on a right helicoid is discussed via Dirac approach. We show how the uncertainty in measurement for observables of maximally entangled system is affected by the total number of constrained particles $$\sigma $$ σ , external magnetic field $$\vec {\mathcal {B}}$$ B → ; as well as by geometric parameters like the pitch$$\rho $$ ρ and the radial position of particles. In doing so we also highlight numeric bounds on the external field strengths to tune both intraparticle and bipartite entanglement and we remark that the bipartite entanglement is more robust to changes in the fields than the intraparticle entanglement, in this framework. We also highlight specific parameter regimes which lead the uncertainty (in measurement) to achieve respective parameter independence and, for a particular subset of commutation relations, the system remains confined in the quantum regime even in the limit $$\sigma \rightarrow \infty $$ σ → ∞ . It is observed that the uncertainties are strongly influenced by the geometric parameters e.g., $$\rho $$ ρ , and the strength of bipartite as well as intraparticle entanglement might be controllable through $$\rho $$ ρ . The energy equation for this setup is obtained and the additional terms are discussed which arise due to quantum correlations, orbit–orbit interaction and the normal Zeeman effect, which leads to the splitting of the energy level into 11 non-degenerate levels. Finally we comment that, a linkage of this phenomenology with Aharonov–Bohm like effect might be possible by strictly confining $$\vec {\mathcal {B}}$$ B → along the central axis of the helicoid.

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Section: Introductionmentioning

confidence: 99%

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

et al. 2022

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“…A similar study in this direction was made in [12] for the Dirac quantization of particle constrained on a helicoid and in [13] for quantizing the dynamics of a free particle on a D-dimensional sphere. A different approach to dualize quantum with geometry in the pilot-wave limit is presented in [14][15][16], and with topological properties in [17]. Dirac quantization on curved spaces adds some additional terms in the Schrödinger equation that can be linked with the curvature of the space or distortion in the energy spectrum.…”

Section: Introductionmentioning

confidence: 99%

Constrained dynamics of maximally entangled bipartite system

Bashir

Wasay

2021

Eur. Phys. J. C

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The classical and quantum dynamics of two particles constrained on $$S^1$$ S 1 is discussed via Dirac’s approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also quantify the upper bound on the external field $$\vec {B}$$ B → such that $$\vec {B}\ge \vec {B}_{upper }$$ B → ≥ B → upper implies no reduction in the product of dispersion pertaining to one subsystem. Further, we report on the cut-off value of the external field $$\vec {B}_{cutoff }$$ B → cutoff , above which the bipartite entanglement is lost and there exists a direct relationship between uncertainty of the composite system and the external field. We note that, in this framework it is possible to tune the external field for entanglement/unentanglement of a bipartite system. Finally, we show that the additional terms arising in the quantum Hamiltonian, due to the requirement of Hermiticity of operators, produce a shift in the energy of the system.

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Intrinsic quantum dynamics of particles in brane gravity

Jalalzadeh

2023

Annals of Physics

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Geometric description of Schrödinger equation in Finsler and Funk geometry

Cited by 3 publications

References 33 publications

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

Constrained dynamics of maximally entangled bipartite system

Intrinsic quantum dynamics of particles in brane gravity

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