arXiv subjects

O. Olendski

Publications and source records attributed to O. Olendski.

At least 19 recordsLinked to original sources

arXiv2023

Quantum-information theory of magnetic field influence on circular dots with different boundary conditions

Influence of the transverse uniform magnetic field $\bf B$ on position (subscript $ρ$) and momentum ($γ$) Shannon quantum-information entropies $S_{ρ,γ}$, Fisher informations $I_{ρ,γ}$ and informational energies $O_{ρ,γ}$ is studied theoretically for the 2D circular quantum dots (QDs) whose circumference supports homogeneous either Dirichlet or Neumann boundary condition (BC). Analysis reveals similarities and differences of the influence on the properties of the structure of the surface interaction with the magnetic field. Conspicuous distinction between the spectra are crossings at the increasing induction of the Neumann energies with the same radial quantum number $n$ and adjacent non-positive angular indices $m$. At the growing $B$, either system undergoes Landau condensation when its characteristics turn into their uniform field counterparts. For the Dirichlet system this transformation takes place at the smaller magnetic intensities; e.g., the Dirichlet sum $S_{ρ_{00}}+S_{γ_{00}}$ on its approach from above to a fundamental limit $2(1+\lnπ)$ is at any $B$ smaller than the corresponding Neumann quantity what physically means that the former geometry provides more total information about the position and motion of the particle. It is pointed out that the widely accepted disequilibrium uncertainty relation $O_ρO_γ\leq(2π)^{-\mathtt{d}}$, with $\mathtt{d}$ being a dimensionality of the system, is violated by the Neumann QD in the magnetic field. Comparison with electrostatic harmonic confinement is performed. Physical interpretation is based on the different roles of the two BCs and their interplay with the field: Dirichlet (Neumann) surface is a repulsive (attractive) interface.

quant-ph↗

arXiv2023

One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory

Motion along semi-infinite straight line in a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered with the emphasis on the analysis of its quantum-information properties. Classical measure of symmetry of the potential is proposed and its dependence on the particle energy and the factor $\mathfrak{a}$ describing a relative strength of its constituents is described; in particular, it is shown that a variation of the parameter $\mathfrak{a}$ alters the shape from the half-harmonic oscillator (HHO) at $\mathfrak{a}=0$ to the perfectly symmetric one of the double frequency oscillator (DFO) in the limit of huge $\mathfrak{a}$. Quantum consideration focuses on the analysis of information-theoretical measures, such as standard deviations, Shannon, Rényi and Tsallis entropies together with Fisher information, Onicescu energy and non--Gaussianity. For doing this, among others, a method of calculating momentum waveforms is proposed that results in their analytic expressions in form of the confluent hypergeometric functions. Increasing parameter $\mathfrak{a}$ modifies the measures in such a way that they gradually transform into those corresponding to the DFO what, in particular, means that the lowest orbital saturates Heisenberg, Shannon, Rényi and Tsallis uncertainty relations with the corresponding position and momentum non--Gaussianities turning to zero. A simple expression is derived of the orbital-independent lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where momentum components of these one-parameter entropies exist which shows that it varies between $1/4$ at HHO and zero when $\mathfrak{a}$ tends to infinity. Physical interpretation of obtained mathematical results is provided.

quant-ph↗

arXiv2022

Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field

Shannon quantum information entropies $S_{ρ,γ}$, Fisher informations $I_{ρ,γ}$, Onicescu energies $O_{ρ,γ}$ and Rényi entropies $R_{ρ,γ}(α)$ are calculated both in the position (subscript $ρ$) and momentum ($γ$) spaces as functions of the inner radius $r_0$ for the two-dimensional Dirichlet unit-width annulus threaded by the Aharonov-Bohm (AB) flux $ϕ_{AB}$. Discussion is based on the analysis of the corresponding position and momentum waveforms. Position Shannon entropy (Onicescu energy) grows logarithmically (decreases as $1/r_0$) with large $r_0$ tending to the same asymptote $S_ρ^{asym}=\ln(4πr_0)-1$ [$O_ρ^{asym}=3/(4πr_0)$] for all orbitals whereas their Fisher counterpart $I_{ρ_{nm}}(ϕ_{AB},r_0$) approaches in the same regime the $m$-independent limit mimicking in this way the energy spectrum variation with $r_0$, which for the thin structures exhibits quadratic dependence on the principal index. Frequency of the fading oscillations of the radial parts of the wave vector functions increases with the inner radius what results in the identical $r_0\gg1$ asymptote for all momentum Shannon entropies $S_{γ_{nm}}(ϕ_{AB};r_0)$ with the alike $n$ and different $m$. The same limit causes the Fisher momentum components $I_γ(ϕ_{AB},r_0)$ to grow exponentially with $r_0$. It is proved that the lower limit $α_{TH}$ of the semi-infinite range of the dimensionless coefficient $α$, where the momentum component of this one-parameter entropy exists, is \textit{not} influenced by the radius; in particular, the change of the topology from the simply, $r_0=0$, to the doubly, $r_0>0$, connected domain is \textit{un}able to change $α_{TH}=2/5$. AB field influence on the measures is calculated too.

cond-mat.mes-hall↗

arXiv2021

Quantum information measures of the Dirichlet and Neumann hyperspherical dots

$\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schrödinger equation in position space and the Fourier transform of the corresponding wave function leads to the analytic form of its momentum counterpart too. This paves the way to an efficient computation in either space of Shannon, Rényi and Tsallis entropies, Onicescu energies and Fisher informations; for example, for the latter measure, some particular orbitals exhibit simple expressions in either space at any BC type. A comparative study of the influence of the edge requirement on the quantum information measures proves that the lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where one-parameter momentum entropies exist is equal to $\mathtt{d}/(\mathtt{d}+3)$ for the Dirichlet hyperball and $\mathtt{d}/(\mathtt{d}+1)$ for the Neumann one what means that at the unrestricted growth of the dimensionality both measures have their Shannon fellow as the lower verge. Simultaneously, this imposes the restriction on the upper value of the interval $[1/2,α_R)$ inside which the Rényi uncertainty relation for the sum of the position $R_ρ(α)$ and wave vector $R_γ\left(\fracα{2α-1}\right)$ components is defined: $α_R$ is equal to $\mathtt{d}/(\mathtt{d}-3)$ for the Dirichlet geometry and to $\mathtt{d}/(\mathtt{d}-1)$ for the Neumann BC. Some other properties are discussed from mathematical and physical points of view. Parallels are drawn to the corresponding properties of the hydrogen atom and similarities and differences are explained based on the analysis of the associated wave functions.

quant-ph↗

arXiv2021

Comparative analysis of information measures of the Dirichlet and Neumann two-dimensional quantum dots

Analytic representation of both position as well as momentum waveforms of the two-dimensional (2D) circular quantum dots with the Dirichlet and Neumann boundary conditions (BCs) allowed an efficient computation in either space of Shannon $S$, Rényi $R(α)$ and Tsallis $T(α)$ entropies, Onicescu energies $O$ and Fisher informations $I$. It is shown that a transition to the 2D geometry lifts the 1D degeneracy of the position components $S_ρ$, $O_ρ$, $R_ρ(α)$. Among many other findings, it is established that the lower limit $α_{TH}$ of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where one-parameter momentum entropies exist is equal to 2/5 for the Dirichlet requirement and 2/3 for the Neumann one. Since their 1D counterparts are $1/4$ and $1/2$, respectively, this simultaneously reveals that this critical value crucially depends not only on the position BC but the dimensionality of the structure too. As the 2D Neumann threshold $α_{TH}^N$ is greater than one half, its Rényi uncertainty relation for the sum of the position and wave vector components $R_ρ(α)+R_γ\left(\fracα{2α-1}\right)$ is valid in the range $[1/2,2)$ only with its logarithmic divergence at the right edge whereas for all other systems it is defined at any coefficient $α$ not smaller than one half. For both configurations, the lowest-energy level at $α=1/2$ does saturate Rényi and Tsallis entropic inequalities. Other properties are discussed and analyzed from the mathematical and physical points of view.

quant-ph↗

arXiv2020

Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells

A comparative analysis of the Dirichlet and Neumann boundary conditions (BCs) of the one-dimensional (1D) quantum well extracts similarities and differences of the Rényi $R(α)$ as well as Tsallis $T(α)$ entropies between these two geometries. It is shown, in particular, that for either BC the dependencies of the Rényi position components on the parameter $α$ are the same for all orbitals but the lowest Neumann one for which the corresponding functional $R$ is not influenced by the variation of $α$. Lower limit $α_{TH}$ of the semi infinite range of the dimensionless Rényi/Tsallis coefficient where {\em momentum} entropies exist crucially depends on the {\em position} BC and is equal to one quarter for the Dirichlet requirement and one half for the Neumann one. At $α$ approaching this critical value, the corresponding momentum functionals do diverge. The gap between the thresholds $α_{TH}$ of the two BCs causes different behavior of the Rényi uncertainty relations as functions of $α$. For both configurations, the lowest-energy level at $α=1/2$ does saturate either type of the entropic inequality thus confirming an earlier surmise about it. It is also conjectured that the threshold $α_{TH}$ of one half is characteristic of any 1D non-Dirichlet system. Other properties are discussed and analyzed from the mathematical and physical points of view.

quant-ph↗

arXiv2019

Rényi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields

One-parameter functionals of the Rényi $R_{ρ,γ}(α)$ and Tsallis $T_{ρ,γ}(α)$ types are calculated both in the position (subscript $ρ$) and momentum ($γ$) spaces for the azimuthally symmetric 2D nanoring that is placed into the combination of the transverse uniform magnetic field $\bf B$ and the Aharonov-Bohm (AB) flux $ϕ_{AB}$ and whose potential profile is modelled by the superposition of the quadratic and inverse quadratic dependencies on the radius $r$. Position (momentum) Rényi entropy depends on the field $B$ as a negative (positive) logarithm of $ω_{eff}\equiv\left(ω_0^2+ω_c^2/4\right)^{1/2}$, where $ω_0$ determines the quadratic steepness of the confining potential and $ω_c$ is a cyclotron frequency. This makes the sum ${R_ρ}_{nm}(α)+{R_γ}_{nm}(\fracα{2α-1})$ a field-independent quantity that increases with the principal $n$ and azimuthal $m$ quantum numbers and does satisfy corresponding uncertainty relation. Analytic expression for the lower boundary of the semi-infinite range of the dimensionless coefficient $α$ where the momentum entropies exist reveals that it depends on the ring geometry, AB intensity and quantum number $m$. It is proved that there is the only orbital for which both Rényi and Tsallis uncertainty relations turn into the identity at $α=1/2$ and which is not necessarily the lowest-energy level. At any coefficient $α$, the dependence of the position Rényi entropy on the AB flux mimics the energy variation with $ϕ_{AB}$ what, under appropriate scaling, can be used for the unique determination of the associated persistent current. Similarities and differences between the two entropies and their uncertainty relations are discussed too.

quant-ph↗

arXiv2019

Quantum information measures of the Aharonov-Bohm ring in uniform magnetic fields

Shannon quantum information entropies $S_{ρ,γ}$, Fisher informations $I_{ρ,γ}$, Onicescu energies $O_{ρ,γ}$ and complexities $e^SO$ are calculated both in position (subscript $ρ$) and momentum ($γ$) spaces for azimuthally symmetric 2D nanoring that is placed into combination of transverse uniform magnetic field $\bf B$ and Aharonov-Bohm (AB) flux $ϕ_{AB}$ and whose potential profile is modeled by superposition of quadratic and inverse quadratic dependencies on radius $r$. Increasing intensity $B$ flattens momentum waveforms $Φ_{nm}({\bf k})$ and in the limit of infinitely large fields they turn to zero, what means that the position wave functions $Ψ_{nm}({\bf r})$, which are their Fourier counterparts, tend in this limit to the $δ$-functions. Position (momentum) Shannon entropy depends on the field $B$ as a negative (positive) logarithm of $ω_{eff}\equiv\left(ω_0^2+ω_c^2/4\right)^{1/2}$, where $ω_0$ determines the quadratic steepness of the confining potential and $ω_c$ is a cyclotron frequency. This makes the sum ${S_ρ}_{nm}+{S_γ}_{nm}$ a field-independent quantity that increases with the principal $n$ and azimuthal $m$ quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on $m$, linearly increases with $n$ and varies as $ω_{eff}$ whereas its $n$ and $m$ dependent Onicescu counterpart ${O_ρ}_{nm}$ changes as $ω_{eff}^{-1}$. The products ${I_ρ}_{nm}{I_γ}_{nm}$ and ${O_ρ}_{nm}{O_γ}_{nm}$ are $B$-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of $ϕ_{AB}$ at $B=0$. An inverse statement is correct too.

quant-ph↗

arXiv2019

Rényi and Tsallis entropies: three analytic examples

A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum Rényi $R(α)$ and Tsallis $T(α)$ entropies, focuses on extracting the most characteristic physical features of these one-parameter functionals. Consideration of the harmonic oscillator reconfirms a special status of the Gaussian distribution: at any parameter $α$ it converts into the equality both Rényi and Tsallis uncertainty relations removing for the latter an additional requirement $1/2\leqα\leq1$ that is a necessary condition for all other geometries. It is shown that the lowest limit of the semi infinite range of the dimensionless parameter $α$ where \emph{momentum} components exist strongly depends on the \emph{position} potential and/or boundary condition for the \emph{position} wave function. Asymptotic limits reveal that in either space the entropies $R(α)$ and $T(α)$ approach their Shannon counterpart, $α=1$, along different paths. Similarities and differences between the two entropies and their uncertainty relations are exemplified. Some unsolved problems are pointed at too.

quant-ph↗

arXiv2018

Electric-Field Control of Bound States and Optical Spectrum in Window-Coupled Quantum Waveguides

Properties of the bound states of two quantum waveguides coupled via the window of the width $s$ in their common boundary are calculated under the assumption that the transverse electric field $\pmb{\mathscr{E}}$ is applied to the structure. It is shown that the increase of the electric intensity brings closer to each other fundamental propagation thresholds of the opening and the arms. As a result, the ground state, which in the absence of the field exists at any nonzero $s$, exhibits the energy $E_0$ decrease for the growing $\mathscr{E}$ and in the high-field regime $E_0$ stays practically the same regardless of the size of the connecting region. It is predicted that the critical window widths $s_{cr_n}$, $n=1,2,\ldots$, at which new excited localized orbitals emerge, strongly depend on the transverse voltage; in particular, the field leads to the increase of $s_{cr_n}$, and, for quite strong electric intensities, the critical width unrestrictedly diverges. This remarkable feature of the electric-field-induced switching of the bound states can be checked, for example, by the change of the optical properties of the structure when the gate voltage is applied; namely, both the oscillator strength and absorption spectrum exhibit a conspicuous maximum on their $\mathscr{E}$ dependence and turn to zero when the electric intensity reaches its critical value. Comparative analysis of the two-dimensional (2D) and 3D geometries reveals their qualitative similarity and quantitative differences.

cond-mat.mes-hall↗

arXiv2018

Quantum information measures of the one-dimensional Robin quantum well

Shannon quantum information entropies $S_{x,k}$, Fisher informations $I_{x,k}$, Onicescu energies $O_{x,k}$ and statistical complexities $e^{S_{x,k}}O_{x,k}$ are calculated both in the position (subscript $x$) and momentum ($k$) representations for the Robin quantum well characterized by the extrapolation lengths $Λ_-$ and $Λ_+$ at the two confining surfaces. The analysis concentrates on finding and explaining the most characteristic features of these quantum information measures in the whole range of variation of the Robin distance $Λ$ for the symmetric, $Λ_-=Λ_+=Λ$, and antisymmetric, $Λ_-=-Λ_+=Λ$, geometries. Analytic results obtained in the limiting cases of the extremely large and very small magnitudes of the extrapolation parameter are corroborated by the exact numerical computations that are extended to the arbitrary length $Λ$. It is confirmed, in particular, that the entropic uncertainty relation $S_{x_n}+S_{k_n}\geq1+\lnπ$ and general inequality $e^SO\geq1$, which is valid both in the position and momentum spaces, hold true at any Robin distance and for every quantum state $n$. For either configuration, there is a range of the extrapolation lengths where the rule $S_{x_{n+1}}(Λ)+S_{k_{n+1}}(Λ)\geq S_{x_n}(Λ)+S_{k_n}(Λ)$ that is correct for the Neumann ($Λ=\infty$) or Dirichlet ($Λ=0$) boundary conditions, is violated. Other analytic and numerical results for all measures are discussed too and their physical meaning is highlighted.

cond-mat.mes-hall↗

arXiv2018

Thermodynamic properties of the one-dimensional Robin quantum well

Thermodynamic properties of Robin quantum well with extrapolation length $Λ$ are analyzed theoretically both for canonical and two grand canonical ensembles with special attention being paid to situation when energies of one or two lowest-lying states are split-off from rest of spectrum by large gap that is controlled by varying $Λ$. For single split-off level, which exists for the geometry with equal magnitudes but opposite signs of Robin distances on confining interfaces, heat capacity $c_V$ of canonical averaging is a nonmonotonic function of temperature $T$ with its salient maximum growing to infinity as $\ln^2Λ$ for decreasing to zero extrapolation length and its position being proportional to $1/(Λ^2\lnΛ)$. Specific heat per particle $c_N$ of Fermi-Dirac ensemble depends nonmonotonically on temperature too with its pronounced extremum being foregone on $T$ axis by plateau whose value at dying $Λ$ is $(N-1)/(2N)k_B$, with $N$ being a number of fermions. Maximum of $c_N$, similar to canonical averaging, unrestrictedly increases as $Λ$ goes to zero and is the largest for one particle. Most essential property of Bose-Einstein ensemble is a formation, for growing number of bosons, of sharp asymmetric shape on the $c_N-T$ characteristics that is more protrusive at the smaller Robin distances. This cusp-like structure is a manifestation of the phase transition to the condensate state. For two split-off orbitals, one additional maximum emerges whose position is shifted to colder temperatures with increase of energy gap between these two states and their higher-lying counterparts and whose magnitude approaches $Λ$-independent value. All these physical phenomena are qualitatively and quantitatively explained by variation of energy spectrum by Robin distance.

cond-mat.mes-hall↗

arXiv2017

Comment on 'Fisher information for quasi-one-dimensional hydrogen atom'

A further argument is provided in the discussion on the correct form of the bound-state momentum wave function of the quasi-one-dimensional hydrogen atom; namely, considering its behavior at the large quantum indices, it is reconfirmed that the complex expression from Olendski (2017) {\it Eur. J. Phys.} {\bf 38} 038001 is a correct one. Groundlessness of other interpretations is also highlighted.

quant-ph↗

arXiv2017

Comment on "On the realisation of quantum Fisher information"

It is shown that calculation of the momentum Fisher information of the quasione- dimensional hydrogen atom recently presented by Saha et al (2017 Eur. J. Phys. {\bf 38} 025103) is wrong. A correct derivation is provided and its didactical advantages and scientific significances are highlighted.

quant-ph↗

arXiv2016

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum-information measures

Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field $\mathscr{E}$ applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length $Λ$ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position $S_x$ and momentum $S_k$ quantum information entropies and their Fisher information $I_x$ and $I_k$ and Onicescu information energies $O_x$ and $O_k$ counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, $Λ=0$ (Neumann, $Λ=\infty$), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum $S_x+S_k$. Analogously, at $Λ=0$ and $Λ=\infty$ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as $\mathscr{E}^{2/3}$ ($\mathscr{E}^{1/3}$) and its inverse, respectively, leading to the field-independent product $I_xI_k$ ($O_xO_k$). Peculiarities of their transformations at the finite nonzero $Λ$ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

quant-ph↗

arXiv2016

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length $Λ$ in the electric field $\mathscr{E}$ that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage-free configuration support negative-energy bound state. For the canonical ensemble, the heat capacity at $Λ<0$ exhibits a nonmonotonic behavior as a function of the temperature $T$ with its pronounced maximum unrestrictedly increasing for the decreasing fields as $\ln^2\mathscr{E}$ and its location being proportional to $(-\ln\mathscr{E})^{-1}$. For the Fermi-Dirac distribution, the specific heat per particle $c_N$ is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the $T$ axis by the plateau whose magnitude at the vanishing $\mathscr{E}$ is defined as $3(N-1)/(2N)k_B$, with $N$ being a number of the particles. The maximum of $c_N$ is the largest for $N=1$ and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose-Einstein ensemble, a formation of the sharp asymmetric feature on the $c_N$-$T$ dependence with the increase of $N$ is shown to be more prominent at the lower voltages. This cusp-like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of $c_N(T)$, is an indication of the phase transition to the condensate state. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.

quant-ph↗

arXiv2016

Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems

A comparative analysis of three different time-independent approaches to studying open quantum structures in uniform electric field $\mathscr{E}$ was performed using the example of one-dimensional attractive or repulsive $δ$-potential and surface that supports the Robin boundary condition. The three considered methods exploit different properties of the scattering matrix $S(\mathscr{E};E)$ as a function of energy $E$: its poles, real values, and zeros of the second derivative of its phase. The essential feature of the method of zeroing the resolvent, which produces complex energies, is the unlimited growth of the wave function at infinity, which is, however, eliminated by the time-dependent interpretation. The real energies at which the unitary scattering matrix becomes real correspond to the largest possible distortion, $S=+1$, or its absence at $S=-1$ which in either case leads to the formation of quasibound states. Depending on their response to increasing electric intensity, two types of field-induced positive energy quasibound levels are identified: electron- and hole-like states. Their evolution and interaction in enlarging field lead ultimately to the coalescence of pairs of opposite states, with concomitant divergence of the associated dipole moments in what is construed as an electric breakdown of the structure. The characteristic features of the coalescence fields and energies are calculated and the behavior of the levels in their vicinity is analyzed. Similarities between the different approaches and their peculiarities are highlighted; in particular, for zero-field bound state in limit of vanishing $\mathscr{E}$, all three methods produce same results, with their outcomes deviating from each other according to growing electric intensity.

cond-mat.mes-hall↗

arXiv2015

Comparative analysis of electric field influence on the quantum wells with different boundary conditions. II. Thermodynamic properties

Thermodynamic properties of the one-dimensional (1D) quantum well (QW) with miscellaneous permutations of the Dirichlet (D) and Neumann (N) boundary conditions (BCs) at its edges in the perpendicular to the surfaces electric field $\mathscr{E}$ are calculated. For the canonical ensemble, analytical expressions involving theta functions are found for the mean energy and heat capacity $c_V$ for the box with no applied voltage. Pronounced maximum accompanied by the adjacent minimum of the specific heat dependence on the temperature $T$ for the pure Neumann QW and their absence for other BCs are predicted and explained by the structure of the corresponding energy spectrum. Applied field leads to the increase of the heat capacity and formation of the new or modification of the existing extrema what is qualitatively described by the influence of the associated electric potential. A remarkable feature of the Fermi grand canonical ensemble is, at any BC combination in zero fields, a salient maximum of $c_V$ observed on the $T$ axis for one particle and its absence for any other number $N$ of corpuscles. Qualitative and quantitative explanation of this phenomenon employs the analysis of the chemical potential and its temperature dependence for different $N$. It is proved that critical temperature $T_{cr}$ of the Bose-Einstein (BE) condensation increases with the applied voltage for any number of particles and for any BC permutation except the ND case at small intensities $\mathscr{E}$ what is explained again by the modification by the field of the interrelated energies. It is shown that even for the temperatures smaller than $T_{cr}$ the total dipole moment $\langle P\rangle$ may become negative for the quite moderate $\mathscr{E}$. For either Fermi or BE system, the influence of the electric field on the heat capacity is shown to be suppressed with $N$ growing.

cond-mat.mes-hall↗