• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • On quantum stochastic master equations
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
October 5, 2026
Africa, Youth, and Civic Dialogue: Public Diplomacy Discussed at HSE University
In late September, HSE University hosted a roundtable discussion titled Civil Society in African Countries and Youth Participation in Public Diplomacy. Representatives of non-governmental organisations from Ghana, Ethiopia, and Russia, along with students from HSE University’s Bachelor’s Programme in Public Administration, discussed how young people without official diplomatic status can influence relations between countries and how the nonprofit sector can remain sustainable amid declining grant funding.
October 1, 2026
HSE Researchers Show How Congenital Motor Disorders Affect Brain Development
Researchers from HSE University’s Institute for Cognitive Neuroscience have synthesised the findings of their previous studies on brain development in children with obstetric brachial plexus palsy and arthrogryposis. Their analysis shows that impaired motor function in early childhood not only limits children’s motor experience but also affects memory, categorical thinking, and information processing. The study has been published in Frontiers in Psychology.
October 1, 2026
Window into the Body: Scientists Develop Neural Network to Detect Risk of 15 Diseases from Retinal Images
Russian universities, with the participation of HSE University, Sber, and Z-union, have developed a neural network that can simultaneously assess the risk of 15 types of pathology from retinal photographs, including not only eye diseases but also cardiovascular conditions. The AI system can help clinicians detect potentially concerning changes at an early stage, identify signs reflecting the condition of retinal blood vessels, and determine whether a patient may need further examination. The paper has been published in Frontiers in Medicine.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

On quantum stochastic master equations

Electronic Journal of Probability. 2025. Vol. 30. Article 57.
Kolokoltsov V.

Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces has been a long standing open problem. The first objective of this paper is to give a solution to this problem under the assumption of bounded operators providing coupling with environment (or a measurement device). Furthermore, recently the author built the theory of the law of large number limit for continuously observed interacting quantum particle systems leading to quantum mean-field games. These limits are described by certain nontrivial extensions of quantum stochastic master equations that can be looked at as infinite-dimensional operator-valued McKean-Vlasov diffusions. The second objective of this paper is to provide a well-posedness result for these new class of McKean-Vlasov diffusions.

Research target: Mathematics Physics
Language: English
Full text
DOI
Text on another site
Keywords: stochastic differential equationsстохастические дифференциальные уравнения с частными производнымиLindblad equationуравнение Линдбладаквантовая фильтрацияquantum filteringquantum interacting particlesквантовые взаимодействующие частицыMcKean-Vlasov diffusion
Similar publications
Prospects for an independent measurement of the l = 1, 2, 3 CMB anisotropy multipoles using the anisotropic Sunyaev-Zel’dovich effect
Осипова А. М., Пилипенко С. В., Novikov D. I. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 063522
We investigate the prospects for observing a specific spectral distortion of the cosmic microwave background, which occurs due to the anisotropy of the radiation when it is scattered by hot plasma of galaxy clusters. Detection of this anisotropic Sunyaev-Zel’dovich effect would enable an independent measurement of the CMB anisotropy multipoles with l 1⁄4 1, 2, 3, allow the ...
Added: October 5, 2026
Explicit Formula for Inverse and Determinant in Geometric Algebras over Odd-dimensional Vector Spaces
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Nanometer thick iron garnet films with high Faraday rotation
Gribova N. I., Osmanov S. V., Lyashko S. D. et al., Journal of Magnetism and Magnetic Materials 2025 No. 614 P. 1–8
Here we demonstrate nanometer thick iron garnet films with high specific Faraday rotation suitable for the magneto-optical applications. Bismuth-substituted iron garnet films of compositions Bi1Y2Fe5O12 and Bi1Tm2Fe5O12 deposited on gadolinium gallium garnet substrate are fabricated and characterized. Their thicknesses range from 2 to 10 nm, which corresponds to just a few crystal lattice constants. Spectacularly, Faraday rotation of the ...
Added: October 4, 2026
On Practical Aspects of Constructing Quasi-Cyclic Subfield Subcodes of Dual Elliptic Codes and Their Application in McEliece-type Cryptosystems
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Enhancement of superconductivity by polarization of magnetic impurities in disordered films
Seleznev G., Fominov Yakov V., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 7 Article 074505
Dirty superconducting films with magnetic impurities can exhibit nontrivial behavior in a magnetic field that polarizes the impurity spins. As predicted by Kharitonov and Feigelman (KF) [JETP Lett. 82, 421 (2005)], this polarization reduces the exchange scattering rate. Consequently, a parallel magnetic field can enhance the critical temperature Tc when magnetic-field pair breaking is weak, as realized for ...
Added: October 2, 2026
Advances in colloidal anisotropic nanocrystals for high-efficiency light-emitting diodes
Zhukov A., Chen F., Zeng Y. et al., Nanoscale 2026 Vol. 18 No. 36 P. 19223–19253
Colloidal semiconductor nanocrystals have emerged as promising materials for next-generation light-emitting diodes (LEDs) owing to their solution processability, tunable emission wavelengths, narrow emission linewidths, and high photoluminescence quantum yields. Among them, anisotropic nanocrystals, including one-dimensional nanorods (NRs) and two-dimensional nanoplatelets (NPLs), offer additional opportunities for controlling transition dipole moment orientation and light out-coupling efficiency. These ...
Added: October 2, 2026
Graphon spin systems as exactly solvable models
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Improved measurement of Born cross sections for chi_bJ omega and chi_bJ (pi+ pi- pi0)non-omega (J = 0, 1, 2) at Belle and Belle II
Uglov T., Pakhlov P., Bodrov D. et al., Journal of High Energy Physics 2026 Vol. 04 Article 101
We study the processes chi_bJ omega and chi_bJ (pi+ pi- pi0)non-omega (J = 0, 1, 2) at center-of-mass energies sqrt(s) from 10.73 to 11.02 GeV using a 142.5 fb^-1 data sample collected with the Belle detector at the KEKB asymmetric-energy e+e- collider; and at sqrt(s) ~ 10.75 GeV using a 19.8 fb^-1 sample collected with ...
Added: October 2, 2026
Observation of e+e- -> eta Upsilon(2S) and search for e+e- -> eta Upsilon(1S), gamma X_b at sqrt(s) near 10.75 GeV
Uglov T., Pakhlov P., Bodrov D. et al., Physical Review Letters 2026 Vol. D No. 113 Article L051102
We present an analysis of the processes e+ e- -> eta Upsilon(1S), eta Upsilon(2S), and gamma X_b with X_b -> pi+ pi- chi_bJ, chi_bJ -> gamma Upsilon(1S) (J = 1, 2) reconstructed from gamma gamma pi+ pi- l+ l- (l = e, mu) final states in 19.6 fb^-1 of Belle II data collected at four ...
Added: October 2, 2026
First Search for B -> Xs nu nubar Decays
Bodrov D., Pakhlova G., Aushev Т. et al., Physical Review Letters 2026 Vol. 136 No. 23 Article 231801
We report the first search for the flavor-changing neutral-current decays B -> Xs nu nubar, where Xs is a hadronic system with strangeness equal to 1, in data collected with the Belle II detector at the SuperKEKB asymmetric-energy e+ e- collider. The data sample corresponds to an integrated luminosity of 365 fb^-1 collected at the ...
Added: October 2, 2026
Search for e+ e- -> gamma chi_bJ (J = 0, 1, 2) near sqrt(s) = 10.746 GeV at Belle II
Pakhlova G., Bodrov D., Aushev Т. et al., Physical Review Letters 2026 Vol. D No. 113 Article 052009
We search for the e+ e- -> gamma chi_bJ (J = 0, 1, 2) processes at center-of-mass energies sqrt(s) = 10.653, 10.701, 10.746, and 10.804 GeV. These data were collected with the Belle II detector at the SuperKEKB collider and correspond to 3.5, 1.6, 9.8, and 4.7 fb^-1 of integrated luminosity, respectively. We set upper ...
Added: October 2, 2026
Measurement of inclusive B -> Xu l nu partial branching fractions and |Vub| at Belle II
Bodrov D., Pakhlova G., Aushev Т. et al., Physical Review Letters 2026 Vol. D No. 113 Article 032004
A sample of 365 fb^-1 of e+ e- -> Upsilon(4S) -> B Bbar data collected by the Belle II experiment is used to measure the partial branching fractions of charmless semileptonic B meson decays and determine the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V_ub. Events containing a signal electron or muon l and a ...
Added: October 2, 2026
Measurement of the CP asymmetry in D0 -> pi+ pi- pi0 decays at Belle II
Bodrov D., Pakhlova G., Aushev Т. et al., Physical Review Letters 2026 Vol. D No. 113 Article 052006
We measure the time- and phase-space-integrated CP asymmetry ACP in D0 -> pi+ pi- pi0 decays reconstructed in e+ e- -> c cbar events collected by the Belle II experiment from 2019 to 2022. This sample corresponds to an integrated luminosity of 428 fb^-1. We require D0 mesons to be produced in D*+ -> D0 ...
Added: October 2, 2026
Study of e+e- -> h+h- J/psi (h = pi, K, p) via initial-state radiation at Belle II
Pakhlov P., Pakhlova G., Bodrov D. et al., Physical Review Letters 2026 Vol. D No. 113 Article 112010
Using a data sample of 427.9 fb^-1 collected by the Belle II detector at or near the Upsilon(4S) and Upsilon(10753) resonances, the cross sections for e+ e- -> h+ h- J/psi (h = pi/K/p) at center-of-mass energies ranging from 3.8 GeV or the production threshold to 5.5/6.0/7.0 GeV have been measured via initial-state radiation. The ...
Added: October 2, 2026
Measurements of the mass difference m(B0) - m(B+) and the energy dependence of the cross-section ratio sigma(e+e- -> B0 Bbar0) / sigma(e+e- -> B+ B-) at Belle and Belle II
Bodrov D., Pakhlova G., Aushev Т. et al., Journal of High Energy Physics 2026 Vol. 05 Article 175
Using data samples collected by the Belle and Belle II experiments at the Upsilon(4S) resonance with integrated luminosities of 571 fb^-1 and 365 fb^-1, respectively, we measure the pseudoscalar B-meson mass difference to be m(B0) - m(B+) = (0.495 +/- 0.024 +/- 0.005) MeV/c^2. The results are based on a simultaneous fit to the variable ...
Added: October 2, 2026
Search for CP violation in Xi_c+ -> Sigma+ h+ h- and Lambda_c+ -> p h+ h- at Belle II
Bodrov D., Pakhlova G., Abumusabh М., Physical Review Letters 2026 Vol. D No. 113 Article 032017
We report decay-rate CP asymmetries of the singly-Cabibbo-suppressed decays Xi_c+ -> Sigma+ h+ h- and Lambda_c+ -> p h+ h-, with h=K, pi, measured using 428 fb^-1 of e+ e- collisions collected by the Belle II experiment at the SuperKEKB collider. The results, ACP(Xi_c+ -> Sigma+ K+ K-) = (3.7 +/- 6.6 +/- 0.6)%, ACP(Xi_c+ ...
Added: October 2, 2026
Планетарное зацепление трилистника
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Study of B+ -> mu+ nu_mu decays at Belle and Belle II
Pakhlov P., Pakhlova G., Bodrov D. et al., Physical Review Letters 2026 Vol. D No. 113 Article 112012
We report a measurement of the branching fraction for the leptonic decay B+ -> mu+ nu_mu. This work presents the first B+ -> mu+ nu_mu result using Belle II data, an updated Belle measurement that supersedes the previous result, and their combination, which yields the most precise search to date. The analysis is based on ...
Added: October 2, 2026
A quantum–analogue formalism for modeling supraliminal information processing
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Search for the Decay B+ -> K+ tau+ tau- Using Data from the Belle and Belle II Experiments
Bodrov D., Pakhlov P., Pakhlova G. et al., Physical Review Letters 2026 Vol. 137 Article 051805
We report a search for the rare decay B+ -> K+ tau+ tau- using 1.2 x 10^9 Upsilon(4S) mesons produced near threshold in electron-positron collisions and collected by the Belle and Belle II experiments. We fully reconstruct the hadronic decay of one B meson produced in the Upsilon(4S) -> B+ B- decay, and search for ...
Added: October 1, 2026
Observation of the Radiative Decay D*_s0(2317)+ -> D*+_s gamma
Bodrov D., Aushev Т., Abumusabh М., Physical Review A: Atomic, Molecular, and Optical physics 2026 No. 136 Article 241901
We report the first observation of the radiative decay D*_s0(2317)+ -> D*+_s gamma with a statistical significance exceeding 10 standard deviations. The signal is observed in the continuum e+ e- -> c c-bar process, using combined data samples of 980.4 fb^-1 from Belle and 427.9 fb^-1 from Belle II, collected at the KEKB and SuperKEKB ...
Added: October 1, 2026
First measurements of the branching fractions for the decay modes Ξ0𝑐 →Λ⁢𝜂 and Ξ0𝑐 →Λ⁢𝜂′ and search for the decay Ξ0𝑐 →Λ⁢𝜋0 using Belle and Belle II data
Bodrov D., Pakhlova G., Aushev Т. et al., Physical Review A: Atomic, Molecular, and Optical physics 2026 Vol. D 113 Article 032015
Using data samples of 988.4 fb^-1 and 427.9 fb^-1 collected with the Belle and Belle II detectors, we present a study of the singly Cabibbo-suppressed decays Xi0_c -> Lambda eta, Lambda eta', and Lambda pi0. We observe the decay Xi0_c -> Lambda eta and find evidence for the decay Xi0_c -> Lambda eta', with corresponding ...
Added: October 1, 2026
Quantum viscosity mechanism of dissipative dynamics in the Dicke model expressed via Lindblad equation of motion
Beck M. E., Seidov S., Mukhin S., Physical Review A: Atomic, Molecular, and Optical physics 2026 Vol. 113 No. 6 Article 063706
Quantum dissipation is studied in the superradiant phase of the extended Dicke model. It is demonstrated analytically by quantum mechanical derivation of the Lindblad equation for the Dicke model in the superradiant state coupled to Caldeira-Leggett thermal bath that the effective viscosity appearing in the semiclassical equations of motion of polaritonic condensate survives in the zero-temperature limit ...
Added: August 13, 2026
On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States
Kolokoltsov V., Russian Journal of Mathematical Physics 2025 Vol. 32 P. 510–529
Quantum filtering equations for mixed states were developed in the eighties of the last century. Since then, the problem of constructing a rigorous mathematical theory for these equations in the basic infinite-dimensional settings has been a challenging open mathematical problem. In a previous paper, the author developed the theory of these equations in the case of bounded coupling operators, ...
Added: December 4, 2025
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit