Spectral filtering in quantum Y-junction (2009)
Cheon, Taksu, Exner, Pavel, Turek, Ondrej
We examine scattering properties of singular vertex of degree $n=2$ and $n=3$, taking advantage of a new form of representing the vertex boundary condition, which has been devised to approximate a...
Approximation of a general singular vertex coupling in quantum graphs (2009)
Cheon, Taksu, Exner, Pavel, Turek, Ondrej
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints...
on graphs and certain Jacobi matrices (2009)
The Erwin, Schrödinger International Boltzmanngasse, Pavel Exner, Pavel Exner
Abstract: The known correspondence between the Kronig–Penney model and certain Jacobi matrices is extended to a wide class of Schrödinger operators on graphs. Examples include rectangular lattices...
Abstract. We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable...
Trotter-Kato product formula for unitary groups (2009)
Exner, Pavel, Neidhardt, Hagen
Let $A$ and $B$ be non-negative self-adjoint operators in a separable Hilbert space such that its form sum $C$ is densely defined. It is shown that the Trotter product formula holds for imaginary...
The distribution of landed property (2009)
Exner, Pavel, Šeba, Petr, Vašata, Daniel
The distribution of property is established through various mechanisms. In this paper we study the acreage distribution of land plots owned by natural persons in the Zl\'{\i}n Region of the Czech...
Post: Convergence of resonances on thin branched quantum wave guides (2008)
Abstract. We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family...
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable...
16th International Congress on Mathematical Physics (2008)
Aizenman, Michael, Daubechies, Ingrid, Exner, Pavel, Froehlich, Juerg, Gallavotti, Giovanni, Sinai, Yakov, ...
QUANTUM NETWORKS MODELLED BY GRAPHS (2008)
Abstract. Quantum networks are often modelled using Schrödinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the...
On the spectrum of a bent chain graph (2008)
Duclos, Pierre, Exner, Pavel, Turek, Ondrej
We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$....
Abstract. The aim of this review is to provide an overview of a recent work concerning “leaky ” quantum graphs described by Hamiltonians given formally by the expression − ∆ − αδ(x −...
A Remark on Helical Waveguides (2008)
Abstract. Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is...
A “hybrid plane ” with spin-orbit interaction (2008)
Pavel Exner, Petr ˇ Seba, In Vladimir, A. Geyler
In this paper we attempt to reconstruct one of the last projects of Volodya Geyler which remained unfinished. We study motion of a quantum particle in the plane to which a halfline lead is attached...
Revised (Day Month Year) We discuss approximations of the vertex coupling on a star-shaped quantum graph of n edges in the singular case when the wave functions are not continuous at the vertex and...
Post: Convergence of resonances on thin branched quantum wave guides (2008)
Abstract. We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family...
Claudio Cacciapuoti, Pavel Exner
In distinction to the Neumann case the squeezing limit of a Dirichlet network leads in the threshold region generically to a quantum graph with disconnected edges, exceptions may come from threshold...
We consider Schr\"odinger operators in $L^2(\mathbb{R}^3)$ with a singular interaction supported by a finite curve $\Gamma$. We present a proper definition of the operators and study their...
We investigate relations between spectral properties of a single-centre point-interaction Hamiltonian describing a particle confined to a bounded domain $\Omega\subset\mathbb{R}^{d},\: d=2,3$, with...
Introduction Though numerous quantum phenomena can be explained by usual semiclassical concepts, a complete theory --- even in the case of the nonrelativistic quantum mechanics --- is certainly...
Jochen Bruning, Pavel Exner, Vladimir A. Geyler
gaps in point-coupled periodic systems of manifolds
Pavel Exner, Kazushi Yoshitomi
In this paper we investigate the operator H fi = \Gamma\Delta \Gamma fi ffi(\Delta \Gamma \Gamma) in L 2
Potential approximations to 0: an inverse Klauder (2007)
Pavel Exner, Hagen Neidhardt, Valentin A. Zagrebnov
a;b
The size distribution of land plots is a result of land allocation processes in the past. In the absence of regulation this is a Markov process leading an equilibrium described by a probabilistic...
Leaky Quantum Graphs: A Review (2007)
The aim of this review is to provide an overview of a recent work concerning ``leaky'' quantum graphs described by Hamiltonians given formally by the expression $-\Delta -\alpha \delta (x-\Gamma)$...
Quantum networks modelled by graphs (2007)
Quantum networks are often modelled using Schroedinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the wave...
A "hybrid plane" with spin-orbit interaction (2007)
In this paper we attempt to reconstruct one of the last projects of Volodya Geyler which remained unfinished. We study motion of a quantum particle in the plane to which a halfline lead is attached...
We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for...
Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide (2007)
Cacciapuoti, Claudio, Exner, Pavel
In distinction to the Neumann case the squeezing limit of a Dirichlet network leads in the threshold region generically to a quantum graph with disconnected edges, exceptions may come from threshold...
A remark on helical waveguides (2007)
Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is known about...
Approximations of singular vertex couplings in quantum graphs (2007)
We discuss approximations of the vertex coupling on a star-shaped quantum graph of $n$ edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation...
On the critical exponent in an isoperimetric inequality for chords (2007)
Exner, Pavel, Fraas, Martin, Harrell II, Evans M.
The problem of maximizing the $L^p$ norms of chords connecting points on a closed curve separated by arclength $u$ arises in electrostatic and quantum--mechanical problems. It is known that among all...
Enhanced binding revisited for a spinless particle in non-relativistic QED (2007)
Catto, Isabelle, Exner, Pavel, Hainzl, Christian
We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a...
Zeno product formula revisited (2007)
Exner, Pavel, Ichinose, Takashi, Neidhardt, Hagen, Zagrebnov, Valentin A.
We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence...
Convergence of resonances on thin branched quantum wave guides (2007)
We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family $X_\eps$ of...
Localization on a quantum graph with a random potential on the edges (2006)
Exner, Pavel, Helm, Mario, Stollmann, Peter
We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the...
Equivalence of resolvent and scattering resonances on quantum graphs (2006)
We discuss resonances for Schr\"odinger operators on metric graphs which consists of a finite compact part and a finite number of halflines attached to it; the vertex coupling is assumed to be of the...
Resonance asymptotics in the generalized Winter model (2006)
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of...
The decay law can have an irregular character (2006)
Within a well-known decay model describing a particle confined initially within a spherical $\delta$ potential shell, we consider the situation when the undecayed state has an unusual energy...
Inequalities for means of chords, with application to isoperimetric problems (2005)
Exner, Pavel, Harrell, Evans M., Loss, Michael
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr\"odinger operator in $L^2(\mathbb{R}^2)$ with an attractive interaction supported on a closed curve...
Necklaces with interacting beads: isoperimetric problems (2005)
We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places $N$ identical point charges at a closed curve $\Gamma$ at the same...
Approximations by graphs and emergence of global structures (2005)
Exner, Pavel, Hejcik, Pavel, Seba, Petr
We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy...
Absolute continuity of the spectrum for periodically modulated leaky wires in $\mathbb{R}^3$ (2005)
Exner, Pavel, Frank, Rupert L.
We consider a model of leaky quantum wire in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically...
Approximations of permutation-symmetric vertex couplings in quantum graphs (2005)
We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with...
Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube (2005)
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the...
On relations between stable and Zeno dynamics in a leaky graph decay model (2005)
Exner, Pavel, Ichinose, Takashi, Kondej, Sylwia
We use a caricature model of a system consisting of a quantum wire and a finite number of quantum dots, to discuss relation between the Zeno dynamics and the stable one which governs time evolution...
Sufficient conditions for the anti-Zeno effect (2005)
The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient conditions under which...
An isoperimetric problem for leaky loops and related mean-chord inequalities (2005)
We consider a class of Hamiltonians in $L^2(\R^2)$ with attractive interaction supported by piecewise $C^2$ smooth loops $\Gamma$ of a fixed length $L$, formally given by...
Zeno product formula revisited (2004)
Exner, Pavel, Ichinose, Takashi, Neidhardt, Hagen, Zagrebnov, Valentin A.
We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence...
Scattering by local deformations of a straight leaky wire (2004)
We consider a model of a leaky quantum wire with the Hamiltonian $-\Delta -\alpha \delta(x-\Gamma)$ in $L^2(\R^2)$, where $\Gamma$ is a compact deformation of a straight line. The existence of wave...
Bose-Einstein Condensation in Geometrically Deformed Tubes (2004)
Exner, Pavel, Zagrebnov, Valentin A.
We show that Bose-Einstein condensate can be created in quasi-one-dimensional systems in a purely geometrical way, namely by bending or other suitable deformation of a tube.
An isoperimetric problem for point interactions (2004)
We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon $\PP_N$. It is shown that the ground state...
Lieb-Thirring inequalities for geometrically induced bound states (2004)
Exner, Pavel, Linde, Helmut, Weidl, Timo
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To...
An approximation to $\delta'$ couplings on graphs (2004)
We discuss a general parametrization for vertices of quantum graphs and show, in particular, how the $\delta'_s$ and $\delta'$ coupling at an $n$ edge vertex can be approximated by means of $n+1$...
Enhanced binding revisited for a spinless particle in non-relativistic QED (2004)
Catto, Isabelle, Exner, Pavel, Hainzl, Christian
We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a...
Schroedinger operators with singular interactions: a model of tunneling resonances (2003)
We discuss a generalized Schr\"odinger operator in $L^2(\mathbb{R}^d), d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It...
Convergence of spectra of graph-like thin manifolds (2003)
We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the...
Leaky quantum wire and dots: a resonance model (2003)
We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in $L^2(\mathbb{R}^2)$ with an attractive singular perturbation supported by a line and a finite number...
Absolute continuity in periodic thin tubes and strongly coupled leaky wires (2003)
Bentosela, Francois, Duclos, Pierre, Exner, Pavel
Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is...
We investigate the operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\mathbb{R}^3)$, where $\Gamma$ is a smooth surface which is either compact or periodic and satisfies suitable regularity...
Bound states due to a strong $\delta$ interaction supported by a curved surface (2002)
We study the Schr\"odinger operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\R^3)$ with a $\delta$ interaction supported by an infinite non-planar surface $\Gamma$ which is smooth, admits a...
Multiple bound states in scissor-shaped waveguides (2002)
Bulgakov, Evgeny N., Exner, Pavel, Pichugin, Konstantin N., Sadreev, Almas F.
We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$....
We study the Laplacian in $L^2(\mathbb{R}^3)$ perturbed on an infinite curve $\Gamma$ by a $\delta$ interaction defined through boundary conditions which relate the corresponding generalized boundary...
Extended Standard Map with Spatio-Temporal Asymmetry (2002)
Cheon, Taksu, Exner, Pavel, Seba, Petr
We analyze the transport properties of a set of symmetry-breaking extensions %, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and temporal asymmetries result in the loss of...
Persistent currents due to point obstacles (2002)
We discuss properties of the two-dimensional Landau Hamiltonian perturbed by a family of identical $\delta$ potentials arranged equidistantly along a closed loop. It is demonstrated that for the loop...
Exner, Pavel, Yoshitomi, Kazushi
We investigate the two-dimensional magnetic Schr\"odinger operator $H_{B,\beta}=(-i\nabla-A)^2 -\beta\delta(\cdot-\Gamma)$, where $\Gamma$ is a smooth loop and the vector potential $A$ corresponds to...
Conference On QMATH ( 8o : 2001 : Taxco, México), Weder, Ricardo (ed.), Exner, Pavel (ed.), Grébert, Benoit (ed.)
Conference On QMATH ( 8o : 2001 : Taxco, México), Weder, Ricardo (ed.), Exner, Pavel (ed.), Grébert, Benoit (ed.)
0-8218-2900-9
Exner, Pavel, Stovicek, Pavel, Vytras, Petr
The most general admissible boundary conditions are derived for an idealised Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard...
Band gap of the Schroedinger operator with a strong delta-interaction on a periodic curve (2001)
Exner, Pavel, Yoshitomi, Kazushi
In this paper we study the operator $H_{\beta}=-\Delta-\beta\delta(\cdot-\Gamma)$ in $L^{2}(\mathbb{R}^{2})$, where $\Gamma$ is a smooth periodic curve in $\mathbb{R}^{2}$. We obtain the asymptotic...
Bound states in point-interaction star-graphs (2001)
Exner, Pavel, Nemcova, Katerina
We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged...
Bound States in Mildly Curved Layers (2001)
Exner, Pavel, Krejcirik, David
It has been shown recently that a nonrelativistic quantum particle constrained to a hard-wall layer of constant width built over a geodesically complete simply connected noncompact curved surface can...
Exner, Pavel, Yoshitomi, Kazushi
In this paper we investigate the operator $H_{\beta}=-\Delta-\beta\delta(\cdot-\Gamma)$ in $L^{2}({\Bbb R}^{2})$, where $\beta>0$ and $\Gamma$ is a closed $C^{4}$ Jordan curve in ${\Bbb R}^{2}$. We...
Quantum mechanics of layers with a finite number of point perturbations (2001)
Exner, Pavel, Nemcova, Katerina
We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character...
Exner, Pavel, Neidhardt, Hagen, Zagrebnov, Valentin
We show that there is a family Schroedinger operators with scaled potentials which approximates the $\delta'$-interaction Hamiltonian in the norm-resolvent sense. This approximation, based on a...
A single-mode quantum transport in serial-structure geometric scatterers (2001)
Exner, Pavel, Tater, Milos, Vanek, David
We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained...
Bound States in Curved Quantum Layers (2001)
Duclos, Pierre, Exner, Pavel, Krejcirik, David
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the...
Geometrically induced spectrum in curved leaky wires (2000)
Exner, Pavel, Ichinose, Takashi
We study measure perturbations of the Laplacian in $L^2(\R^2)$ supported by an infinite curve $\Gamma$ in the plane which is asymptotically straight in a suitable sense. We show that if $\Gamma$ is...
Bound states of infinite curved polymer chains (2000)
We investigate an infinite array of point interactions of the same strength in R^d, d=2,3, situated at vertices of a polygonal curve with a fixed edge length. We demonstrate that if the curve is not...
We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field $B$ parallel to the surface axis. Depending on $B$ and the surface...
Duclos, Pierre, Exner, Pavel, Meller, Bernhard
We discuss the Noeckel model of an open quantum dot, i.e., a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, there are embedded...
Waveguides coupled through a semitransparent barrier: a Birman-Schwinger analysis (2000)
Exner, Pavel, Krejcirik, David
The paper is devoted to a model of a mesoscopic system consisting of a pair of parallel planar waveguides separated by an infinitely thin semitransparent boundary modeled by a transverse delta...
Berry phase for a potential well transported in a homogeneous magnetic field (2000)
Exner, Pavel, Geyler, Vladimir A.
We consider a two-dimensional particle of charge $e$ interacting with a homogeneous magnetic field perpendicular to the plane and a potential well which is transported along a closed loop in the...
Wave Function Shredding by Sparse Quantum Barriers (2000)
Cheon, Taksu, Exner, Pavel, Seba, Petr
We discuss a model in which a quantum particle passes through $\delta$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic...
Berry phase in magnetic systems with point perturbations (1999)
Exner, Pavel, Geyler, Vladimir A.
We study a two-dimensional charged particle interacting with a magnetic field, in general non-homogeneous, perpendicular to the plane, a confining potential, and a point interaction. If the latter...
Magnetic strip waveguides (1999)
We analyze the spectrum of the "local" Iwatsuka model, i.e. a two-dimensional charged particle interacting with a magnetic field which is homogeneous outside a finite strip and translationally...
Anomalous Pauli electron states for magnetic fields with tails (1999)
Exner, Pavel, Hirokawa, Masao, Ogurisu, Osamu
We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results...
Point interactions in a tube (1999)
We discuss discuss spectral and scattering properties of a particle confined to a straight Dirichlet tube in $\mathbb{R}^3$ with a family of point interactions.
Edge currents in the absence of edges (1999)
Exner, Pavel, Joye, Alain, Kovarik, Hynek
We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely...
Optimal eigenvalues for some Laplacians and Schr\"odinger operators depending on curvature (1999)
Exner, Pavel, Harrell, Evans M., Loss, Michael
This article is an expanded version of the plenary talk given by Evans Harrell at QMath98, a meeting in Prague, June 1998. We consider Laplace operators and Schr\"odinger operators with potentials...
Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature (1999)
Pavel Exner, Evans M. Harrell, Michael Loss
We consider Laplace operators and Schrödinger operators with potentials containing curvature on certain regions of nontrivial topology, especially closed curves, annular domains, and shells....
Stability of driven systems with growing gaps, Quantum rings and Wannier ladders (1998)
Asch, Joachim, Duclos, Pierre, Exner, Pavel
We consider a quantum particle in a periodic structure submitted to a constant external electromotive force. The periodic background is given by a smooth potential plus singular point interactions...
On the number of particles which a curved quantum waveguide can bind (1998)
Exner, Pavel, Vugalter, Simeon A.
We discuss the discrete spectrum of N particles in a curved planar waveguide. If they are neutral fermions, the maximum number of particles which the waveguide can bind is given by a one-particle...
Probability current tornado loops in three-dimensional scattering (1997)
We consider scattering of a three-dimensional particle on a finite family of delta potentials. For some parameter values the scattering wavenctions exhibit nodal lines in the form of closed loops,...
Evanescent modes in a multiple scattering factorization (1997)
We discuss differences between the exact S-matrix for scattering on serial structures and a known factorized expression constructed of single-element S-matrices. As an illustration, we use an exactly...
Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers (1997)
Exner, Pavel, Vugalter, Simeon
We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in the common boundary....
Magnetoresonances on a lasso graph (1997)
We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to...
Contact Interactions on Graph Superlattices (1996)
this paper is to show that they represent in a sense a counterpart to the coupling given by (1.1), and that they generalize naturally the concept of ffi
Weakly Coupled States on Branching Graphs (1996)
. We consider a Schrodinger particle on a graph consisting of N links joined at a single point. Each link supports a real locally integrable potential V j ; the self--adjointness is ensured by the...
Weakly coupled states on branching graphs (1995)
We consider a Schr\"odinger particle on a graph consisting of $\,N\,$ links joined at a single point. Each link supports a real locally integrable potential $\,V_j\,$; the self--adjointness is...
Band spectra of rectangular graph superlattices (1995)
We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is...
Contact interactions on graph superlattices (1995)
We consider a quantum mechanical particle living on a graph and discuss the behaviour of its wavefunction at graph vertices. In addition to the standard (or delta type) boundary conditions with...
A duality between Schroedinger operators on graphs and certain Jacobi matrices (1995)
The known correspondence between the Kronig-Penney model and certain Jacobi matrices is extended to a wide class of Schroedinger operators on graphs. Examples include rectangular lattices with and...
Curvature-Induced Bound States In Quantum Waveguides In Two And Three Dimensions (1995)
Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated. It is shown that if the tube is non--straight and its curvature vanishes asymptotically,...
The absence of the absolutely continuous spectrum for delta' Wannier-Stark Ladders (1995)
The Erwin, Schrodinger International Pasteurgasse, Pavel Exner, P. Exner
Introduction One--dimensional Schrodinger operators with potentials composed of a periodic and an aperiodic, most often linear, part have been studied by many authors --- see, e.g., [4, 7, 8, 10] and...
Pierre Duclos, Pavel Exner, Bernhard Meller
from perturbed symmetry in open quantum dots
The size distribution of land plots is a result of land allocation processes in the past. In the absence of regulation this is a Markov process leading an equilibrium described by a probabilistic...