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SUMMARY:Resonant tunneling through one-point singular potentials
DTSTART;VALUE=DATE-TIME:20260924T110000Z
DTEND;VALUE=DATE-TIME:20260924T112000Z
DTSTAMP;VALUE=DATE-TIME:20260914T055056Z
UID:indico-contribution-533@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Alexander Zolotaryuk ()\nIn one-dimensional quantum 
 mechanics\, shrinking a system to isolated points (set of Lebesgue's measu
 re zero) leads to exactly solvable models. These models are referred to as
  point (contact or zero-range) interactions (PIs). In these cases\,resolve
 nts and spectra of Schroedinger operators\, scattering coefficients  and o
 ther characteristics can analytically be computed. Currently\, because of 
 the rapid progress in fabricating nanoscale quantum devices\, of particula
 r importance is the point modeling of different structures like quantum wa
 veguides\, spectral filters\, or infinitesimally thin sheets.\n \nWe have 
 initiated a new project in the domain of PIs regarding a resonant tunnelin
 g through zero-range potentials being more singular than a traditional Dir
 ac's delta potential. A typical example is the distributional potential in
  the form of a spatial derivative of the delta function. \n\nUsing here a 
 very simple two-scale (two-parameter) regularization scheme\, we observe t
 hat different pathways $\\Delta'_{\\varepsilon}(x) \\to \\delta'(x)$ as $\
 \varepsilon \\to 0$ realize different PIs with the following three types o
 f boundary conditions on the wave function $\\psi(x)$: \ni)  $\\psi(-0) =\
 \psi(+0)=0$ (separated with  full reflection)\; \nii) $\\psi(+0)=\\theta_n
  \\psi(-0)\,~~\\psi'(+0) = \\theta_n^{-1}\\psi'(-0)$\, $\\theta_n \\in R$\
 , $n \\in Z$ (non-separated with resonant tunneling)\; \niii) $\\psi(+0)=\
 \theta_n \\psi(-0)\,~~\\psi'(+0) = \\alpha_n \\psi(-0)\n+\\theta_n^{-1}\\p
 si'(-0)\,$  $\\alpha_n \\in R $ (non-separated with resonant tunneling hav
 ing a single bound state at each $n$).\nFor each of these types\, the regi
 ons on the plane of two squeezing parameters are \nindicated explicitly.\n
 \n  Recent literature:\n\n1. A.V. Zolotaryuk and Y. Zolotaryuk\, ``Scatter
 ing data and bound states of \na squeezed double-layer structure''\,  *J. 
 Phys. A: Math. Theor.*  **54** (2021) \n035201\; [doi.org/10.1088/1751-812
 1/abd156][1]   \n2. Y. Zolotaryuk and A.V. Zolotaryuk\, ``Influence of a s
 queezed prewell \non tunneling properties and bound states in heterostruct
 ures''\,\n*Annals of Physics* **477** (2025) 169999\; [doi.org/10.1016/j.a
 op.2025.169999][2] \n3. Y. Zolotaryuk and A.V. Zolotaryuk\, ``Conditions f
 or perfect transmission of quantum particles across layered heterostructur
 es and resonance effects of an auxiliary well potential''\, *Front. Appl. 
 Math. Stat.* **11** (2015) 1636414\;\n[doi.org/10.3389/fams.2025.1636414][
 3]\n\n\n  [1]: http://doi.org/10.1088/1751-8121/abd156\n  [2]: http://doi.
 org/10.1016/j.aop.2025.169999\n  [3]: http://doi.org/10.3389/fams.2025.163
 6414\n\nhttps://indico.bitp.kiev.ua/event/18/contributions/533/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/533/
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