${\mathsf D}^2={\mathsf H}+1/4$ with point interactions

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Posilicano, A., Reginato, L.
Format:	Preprint
Published:	2023
Subjects:	Mathematical Physics Analysis of PDEs
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Scattering theory with both regular and singular perturbations
by: Mantile, Andrea, et al.
Published: (2022)

Body resonances for classical waves
by: Mantile, Andrea, et al.
Published: (2024)

Resolvent, spectrum and resonances for the acoustic operator with piecewise constant coefficients
by: Mantile, Andrea, et al.
Published: (2026)

Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction
by: Forcella, Luigi, et al.
Published: (2024)

On the resolvent of $H+A^{*}+A$
by: Posilicano, Andrea
Published: (2023)

Two dimensional NLS ground states with attractive Coulomb potential and point interaction
by: Boni, Filippo, et al.
Published: (2023)

Microscopic derivation of a Schrödinger equation in dimension one with a nonlinear point interaction
by: Adami, Riccardo, et al.
Published: (2023)

Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system
by: Collot, Charles, et al.
Published: (2024)

Existence of non-Abelian vortices in a coupled 4D-2D quantum field theory
by: Xu, Yilu, et al.
Published: (2024)

Faber-Krahn inequalities for Schrödinger operators with point and with Coulomb interactions
by: Lotoreichik, Vladimir, et al.
Published: (2020)

Nonlinear diffusion limit of non-local interactions on a sphere
by: Peletier, Mark A., et al.
Published: (2025)

On Moffatt's magnetic relaxation for 2D and 2.5D flows
by: Mohammadkhani, Sepehr, et al.
Published: (2025)

Stationary phase with Cauchy singularity. A critical point of signature $(+,-)$
by: Klein, Christian, et al.
Published: (2026)

Dynamics of point-vortex type systems near thermal equilibrium: relaxation or not?
by: Duerinckx, Mitia, et al.
Published: (2024)

On a repulsion model with Coulomb interaction and nonlinear mobility
by: de Courcel, Antonin Chodron, et al.
Published: (2025)

Emergence of fermion-mediated interactions in Bose-Fermi mixtures
by: Cárdenas, Esteban, et al.
Published: (2025)

Point interactions and singular solutions to semilinear elliptic equations
by: Boni, Filippo, et al.
Published: (2026)

On two systems of Burgers type arising in nonlinear wave interaction
by: Alonso-Orán, Diego, et al.
Published: (2024)

A duality method for mean-field limits with singular interactions
by: Bresch, Didier, et al.
Published: (2024)

The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in $H^\frac{7}{4}(\mathbb{R}^2)$
by: An, Xinliang, et al.
Published: (2022)

Generalised solutions to linear and non-linear Schrödinger-type equations with point defect: Colombeau and non-Colombeau regimes
by: Dugandžija, N., et al.
Published: (2022)

The Second Order 2D Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime
by: Chen, Xuwen, et al.
Published: (2024)

Turbulent solutions of the binormal flow and the 1D cubic Schrödinger equation
by: Banica, Valeria, et al.
Published: (2024)

Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions
by: Braides, Andrea, et al.
Published: (2025)

Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction
by: Hadama, Sonae, et al.
Published: (2024)

Mountain-Pass Solutions in 2D Turbulence with Generalized Sobolev Operators
by: Santos, Rômulo Damasclin Chaves dos
Published: (2024)

Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit
by: Knobel, Niklas
Published: (2024)

A new stability result for the 2D Boussinesq equations with horizontal dissipation
by: Jin, Hong Sung, et al.
Published: (2023)

On ground states for the 2D Schrodinger equation with combined nonlinearities and harmonic potential
by: Carles, Rémi, et al.
Published: (2021)

Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
by: Mengual, Francisco, et al.
Published: (2026)

Radiation damping of the soliton internal mode in 1D quadratic Klein-Gordon equation
by: Bizoń, Piotr, et al.
Published: (2026)

Mean field, hydrodynamic and graph limits for deterministic interacting particle systems: a survey with quantitative estimates
by: Paul, Thierry, et al.
Published: (2022)

Derivation of the compressible Euler equations from the dynamics of interacting Bose gas in the hard-core limit regime
by: Chong, Jacky, et al.
Published: (2024)

Existence and (in)stability of standing waves for the nonlinear Schrödinger Equations on looping-edge graphs with $δ'$-type interactions
by: Pava, Jaime Angulo, et al.
Published: (2026)

A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds
by: Bulut, Aynur, et al.
Published: (2020)

Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation
by: Chen, Xuwen, et al.
Published: (2026)

Creation of chaos for interacting Brownian particles
by: Bernou, Armand, et al.
Published: (2025)

Conditonal Lipschitz stability for the Inverse Problem of the 2D Navier-Stokes System in a Bounded Domain
by: Fan, Jishan, et al.
Published: (2026)

On gap properties for the linearized 1D Dirac--Soler model
by: Aldunate, Danko, et al.
Published: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"914e4c2a006e7518e56078f8239b1725"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790782736.624 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "914e4c2a006e7518e56078f8239b1725" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=914e4c2a006e7518e56078f8239b1725; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"18785"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2304_09130/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2304_09130/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790782736.6195
REQUEST_TIME	1790782736

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"914e4c2a006e7518e56078f8239b1725"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790782736.624 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "914e4c2a006e7518e56078f8239b1725" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=914e4c2a006e7518e56078f8239b1725; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"18785"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2304_09130/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2304_09130/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790782736.6195
REQUEST_TIME	1790782736

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: