We investigate electron transport in one dimension from the quantum-acoustic perspective, where the coherent-state representation of lattice vibrations results in a time-dependent deformation potential whose rate is set by the sound speed, fluctuation spectrum is set by the temperature, and overall amplitude is set by the electron-lattice coupling strength. We introduce an acceleration-based adiabatic criterion, consistent with the adiabatic theorem and Landau-Zener theory, that separates adiabatic and diabatic dynamics across the $(T,v)$ plane. The discrete classification agrees with a continuous mean-squared acceleration scale and correlates with a coherence measure given by the ratio of coherence length to the initial packet width $L_φ(t)/σ_0$ . We identify a broad Planckian domain in which the dimensionless diffusivity $α\!=\!Dm/\hbar$ is of order unity and only weakly depends on the parameters. This domain is more prevalent in diabatic regions and in areas of reduced phase coherence, indicating a dephasing driven crossover from Anderson localization to Planckian diffusion. Using the Einstein relation together with nearly constant $α$ , we directly obtain a low temperature tendency $1/τ_{\rm tr}\propto T$ , offering a insight to $T$ -linear resistivity in strange metals. These results provide a unified picture that links adiabaticity, dephasing, and Planckian diffusion in dynamically disordered quantum-acoustics.We investigate electron transport in one dimension from the quantum-acoustic perspective, where the coherent-state representation of lattice vibrations results in a time-dependent deformation potential whose rate is set by the sound speed, fluctuation spectrum is set by the temperature, and overall amplitude is set by the electron-lattice coupling strength. We introduce an acceleration-based adiabatic criterion, consistent with the adiabatic theorem and Landau-Zener theory, that separates adiabatic and diabatic dynamics across the $(T,v)$ plane. The discrete classification agrees with a continuous mean-squared acceleration scale and correlates with a coherence measure given by the ratio of coherence length to the initial packet width $L_φ(t)/σ_0$. We identify a broad Planckian domain in which the dimensionless diffusivity $α\!=\!Dm/\hbar$ is of order unity and only weakly depends on the parameters. This domain is more prevalent in diabatic regions and in areas of reduced phase coherence, indicating a dephasing driven crossover from Anderson localization to Planckian diffusion. Using the Einstein relation together with nearly constant $α$, we directly obtain a low temperature tendency $1/τ_{\rm tr}\propto T$, offering a insight to $T$-linear resistivity in strange metals. These results provide a unified picture that links adiabaticity, dephasing, and Planckian diffusion in dynamically disordered quantum-acoustics.

quant-pharXiv:2512.06263Dec 9, 20250 citations

Classical-quantum Interface of a Particle in a Time-dependent Linear Potential

L. Krache, Mustapha Maamache, Y. Saadi

International Journal of Theoretical PhysicsFeb 23, 20102 citations

Generation of Schrödinger cat type states in a planar semiconductor heterostructure

Jarosław Pawłowski, M. Górski, G. Skowron +1 more

We propose a nanodevice based on a typical planar semiconductor heterostructure with lateral confinement potential created by voltages applied to local gates. We show how to obtain near parabolical confinement along the nanodevice, and how to use coherent states of the harmonic oscillator for spatial separation of electron densities corresponding to opposite spin directions. In such a way, an entangled state of Schr\"odinger's cat type is created. We have performed simulations of a realistic nanodevice model by numerically solving the time-dependent Schr\"odinger equation together with simultaneous tracking of the controllable confinement potential via solution of the Poisson's equation at every time step.We propose a nanodevice based on a typical planar semiconductor heterostructure with lateral confinement potential created by voltages applied to local gates. We show how to obtain near parabolical confinement along the nanodevice, and how to use coherent states of the harmonic oscillator for spatial separation of electron densities corresponding to opposite spin directions. In such a way, an entangled state of Schr\"odinger's cat type is created. We have performed simulations of a realistic nanodevice model by numerically solving the time-dependent Schr\"odinger equation together with simultaneous tracking of the controllable confinement potential via solution of the Poisson's equation at every time step.

arXiv:1610.06482Physical review. B./Physical review. BSep 18, 201711 citations

Generalized Coherent States of a Particle in a Time-Dependent Linear Potential

L. Krache, Mustapha Maamache, Y. Saadi +1 more

We derive, with an invariant operator method and unitary transformation approach, that the Schrödinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states |ϕα,λ( t )⟩ having classical motion. The qualitative properties of the invariant eigenvalue spectrum (discrete or continuous) are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that, for a discrete eigenvalue spectrum, the states |ϕα, n ( t )⟩ could be obtained from the coherent state |ϕα,0( t )⟩.We derive, with an invariant operator method and unitary transformation approach, that the Schrödinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states |ϕα,λ( t )⟩ having classical motion. The qualitative properties of the invariant eigenvalue spectrum (discrete or continuous) are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that, for a discrete eigenvalue spectrum, the states |ϕα, n ( t )⟩ could be obtained from the coherent state |ϕα,0( t )⟩.

Chinese Physics LettersJul 1, 20093 citations

Coherent states of an electron in a quantized electromagnetic wave

Vladislav G. Bagrov, Иосиф Львович Бухбиндер, Dmitri M Gitman +1 more

Theoretical and Mathematical PhysicsDec 1, 19772 citations

(T,v)

plane. The discrete classification agrees with a continuous mean-squared acceleration scale and correlates with a coherence measure given by the ratio of coherence length to the initial packet width

L_φ(t)/σ_0

. We identify a broad Planckian domain in which the dimensionless diffusivity

α\!=\!Dm/\hbar

is of order unity and only weakly depends on the parameters. This domain is more prevalent in diabatic regions and in areas of reduced phase coherence, indicating a dephasing driven crossover from Anderson localization to Planckian diffusion. Using the Einstein relation together with nearly constant

α

, we directly obtain a low temperature tendency

1/τ_{\rm tr}\propto T

, offering a insight to

T

-linear resistivity in strange metals. These results provide a unified picture that links adiabaticity, dephasing, and Planckian diffusion in dynamically disordered quantum-acoustics.