Research interests of Alexander Pechen include diverse topics in mathematics of quantum technologies, dynamics and control of quantum systems. Some results include:
* Proved Turing uncomputability for quantum control (with D. Bondar, Sci. Rep.20).
* Proposed a scheme for incoherent control of open quantum systems using engineered environments (with H. Rabitz, PRA06). In relation to this work, showed that open quantum systems are approximately controllable in the set of all density matrices when driven by coherent and incoherent controls (PRA11).
* Proposed a general scheme for using back-action of non-selective quantum measurements for controlling quantum systems (PRA06). Found exact analytical optimal solutions for various models, including optimal approximation of the quantum anti-Zeno effect by a finite number of quantum measurements.
* Analysed quantum control landscapes for open quantum systems. Proved under certain assumptions the absence of traps in regular points for open quantum systems. These results were applied to the analysis of control in chemistry and biology forming a basis for OptiChem and OptiEvo theories.
* Found the existence of traps for controlling three-level Lambda-atom (with D.J. Tannor). Proved absence of traps for a qubit and for controlling transmission of particle in one-dimensional potential---the first result about trap-free behaviour for quantum systems with infinite-dimensional Hilbert space.
* Derived generalized quantum stochastic differential equations with quantum multipole noise for the dynamics of quantum system interacting with bosonic reservoir beyond the weak coupling limit (with I.V. Volovich).
* Developed a new method for derivation of quantum quantum stochastic differential equations for open quantum systems interacting with a dilute quantum gas. Discovered the appearance of free white noise for such systems thereby finding a new connection of the non-commutative free probability with physics.
Biography
Alexander Pechen received M.Sc. degree with Honour in Physics from Lomonosov Moscow State University (2001) and Ph.D. degree in Mathematical Physics from Steklov Mathematical Institute of Russian Academy of Sciences (2004; thesis advisor Prof. I. V. Volovich). In 2005–2010 he worked as a Research Associate with Prof. H. Rabitz at the Department of Chemistry in Princeton University, where his research was honoured with Blavatnik award for “developing a single, unified mathematical treatment for a wide range of open system control phenomena.” After Princeton he received a Marie Curie International Incoming Fellowship and spent two years in Weizmann Institute of Science working with Prof. D. J. Tannor. He was a visiting scientist at the University of Rome "Tor Vergata" (visiting Prof. L. Accardi) and National Autonomous University of Mexico (visiting Prof. R. Quezada). Now Prof. Pechen works on a variety of topics in quantum control and quantum mechanics as Head of Department of Mathematical Methods for Quantum Technologies in Steklov Mathematical Institute of Russian Academy of Sciences and as Leading Researcher in the National University of Science and Technology "MISIS".
A. N. Pechen, D. J. Tannor, “Are there traps in quantum control landscapes?”, Phys. Rev. Lett., 106 (2011), 120402 , 3 pp., This paper has been selected for the Editor's choice section of Science magazine, vol. 332, p. 514 (29 April 2011): “Look Out for Traps”, by Jake S. Yeston, arXiv: 1508.05434
A. Pechen, “Engineering arbitrary pure and mixed quantum states”, Phys. Rev. A, 84:4 (2011), 042106 , 6 pp., arXiv: 1210.2281
A. Pechen, H. Rabitz, “Teaching the environment to control quantum systems”, Phys. Rev. A, 73 (2006), 062102 , 6 pp., arXiv: quant-ph/0609097
A. Pechen, N. Il'in, F. Shuang, H. Rabitz, “Quantum control by von Neumann measurements”, Phys. Rev. A, 74 (2006), 052102 , 7 pp., arXiv: quant-ph/0606187
L. Accardi, A. Pechen, I. V. Volovich, “A stochastic golden rule and quantum Langevin equation for the low density limit”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6:3 (2003), 431–453 , arXiv: math-ph/0206032
O. V. Morzhin, A. N. Pechen, “On Reachable and Controllability Sets for Time-Minimal Control of an Open Two-Level Quantum System”, Mathematics of quantum technologies, Collected papers, Tr. Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021 (to appear)
2.
K. A. Lyakhov, A. N. Pechen, “Constrained Optimization Criterion for Zirconium Isotopes Separation by the Laser Assisted Retardation of Condensation Method”, Mathematics of quantum technologies, Collected papers, Tr. Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021 (to appear)
3.
G. G. Amosov, A. S. Mokeev, A. N. Pechen, “Noncommutative graphs based on finite-infinite system couplings: Quantum error correction for a qubit coupled to a coherent field”, Phys. Rev. A, 103:4 (2021), 042407 , 17 pp. ;
4.
Matematika kvantovykh tekhnologii, Sbornik statei, Trudy MIAN, 313, ed. A. N. Pechen, I. V. Volovich, G. G. Amosov, A. E. Teretenkov, MIAN, M., 2021
2020
5.
D. I. Bondar, A. N. Pechen, “Uncomputability and complexity of quantum control”, Scientific Reports, 10 (2020), 1195 , 10 pp., arXiv: 1907.10082 (cited: 1)
6.
S. N. Filippov, G. N. Semin, A. N. Pechen, “Quantum master equations for a system interacting with a quantum gas in the low-density limit and for the semiclassical collision model”, Phys. Rev. A, 101 (2020), 12114 , 10 pp., arXiv: 1908.11202 (cited: 4) (cited: 4);
7.
G. G. Amosov, A. S. Mokeev, A. N. Pechen, “Non-commutative graphs and quantum error correction for a two-mode quantum oscillator”, Quantum Information Processing, 19:3 (2020), 95 , 12 pp. (cited: 4) (cited: 4);
8.
K. A. Lyakhov, A. N. Pechen, “CO$_2$ laser system design for efficient boron isotope separation by the method of selective laser-assisted retardation of condensation”, Applied Physics B, 126 (2020), 141 , 11 pp. (cited: 1) (cited: 1);
9.
O. V. Morzhin, A. N. Pechen, “Maximization of the Uhlmann–Jozsa Fidelity for an Open Two-Level Quantum System with Coherent and Incoherent Controls”, Phys. Part. Nucl., 51:4 (2020), 464–469 (cited: 1) (cited: 1)
10.
O. V. Morzhin, A. N. Pechen, “Machine Learning for Finding Suboptimal Final Times and Coherent and Incoherent Controls for an Open Two-Level Quantum System”, Lobachevskii J. Math., 41:12 (2020), 2353–2368;
11.
K. A. Lyakhov, A. N. Pechen, “Evolution of the Enrichment Factor for an Iterative Scheme of Zirconium Isotopes Separation”, Lobachevskii J. Math., 41:12 (2020), 2345–2351;
2019
12.
Oleg V. Morzhin, Alexander N. Pechen, “Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls”, Internat. J. Theoret. Phys., 2019, 1–9 (Published online) , arXiv: 1909.09400 (cited: 5)
13.
Gerard McCaul, Alexander Pechen, Denys I. Bondar, “Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems”, Phys. Rev. E, 99:6 (2019), 062121 , 9 pp., arXiv: 1904.03473
14.
O. V. Morzhin, A. N. Pechen, “Krotov method for optimal control of closed quantum systems”, Russian Math. Surveys, 74:5 (2019), 851–908 (cited: 4) (cited: 3)
15.
O. V. Morzhin, A. N. Pechen, “Maximization of the overlap between density matrices for a two-level open quantum system driven by coherent and incoherent controls”, Lobachevskii J. Math., 40:10 (2019), 1532–1548rdcu.be/b8DB9 (cited: 4) (cited: 4)
16.
K. A. Lyakhov, A. N. Pechen, “Basic Vacuum Pump System Prerequisites for Boron Isotopes Separation by the Laser Assisted Retardation of Condensation (SILARC) method”, Physical and Chemical Processes in Atomic Systems, XVII International Scientific Conference and School of Young Scholars (Moscow, Russia, 2019, Oct’28-30), NRNU MEPhI, 2019, 67https://pnasc.mephi.ru/wp-content/uploads/2019/10/tp_final.pdf
17.
K. A. Lyakhov, A. N. Pechen, H. J. Lee, “Optimal CO2 laser system design for 11BCl3 excitation by the method of selective laser assisted retardation of condensation”, J. Electr. Eng. Electron. Technol., 8 (2019), 86;
2018
18.
N. B. Il'in, A. N. Pechen', “Critical point in the problem of maximizing the transition probability using measurements in an $n$-level quantum system”, Theoret. and Math. Phys., 194:3 (2018), 384–389
19.
N. B. Ilin, A. N. Pechen, “Conditions for the absence of local extrema in problems of quantum coherent control”, Proc. Steklov Inst. Math., 301 (2018), 109–113 (cited: 1) (cited: 2)
20.
A. S. Avanesov, D. A. Kronberg, A. N. Pechen, “Active beam splitting attack applied to differential phase shift quantum key distribution protocol”, P-Adic Numbers Ultrametric Anal. Appl., 10:3 (2018), 222–232 , arXiv: 1910.08339 (cited: 6) (cited: 7)
21.
K. A. Lyakhov, A. N. Pechen, H.-J. Lee, “The efficiency of one-line versus multi-line excitation of boron isotopes within the method of selective laser assisted retardation of condensation”, AIP Advances, 8:9 (2018), 95325 , 10 pp. (cited: 4) (cited: 6)
22.
A. N. Pechen, “Some Methods of Construction of Controls for Quantum Systems”, Quantum probability, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 151, VINITI, Moscow, 2018, 67–72
23.
K. A. Lyakhov, A. N. Pechen, “Objective Function in the Problem of Optimal Laser-Assisted Separation of Isotopes by the Method of Selective Retardation of Condensation”, Quantum probability, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 151, VINITI, Moscow, 2018, 62–66
24.
A. N. Pechen, “International Congress of Mathematicians 2018 : from Rio de Janeiro to St. Petersburg”, Russian Math. Surveys, 73:6 (2018), 1145–1153
2017
25.
A. N. Pechen, N. B. Ilin, “Control landscape for ultrafast manipulation by a qubit”, Journal of Physics A: Mathematical and Theoretical, 50:7 (2017), 75301 , 14 pp., arXiv: 1909.09216 (cited: 4) (cited: 5)
26.
K. A. Lyakhov, H. J. Lee, A. N. Pechen, “Some issues of industrial scale boron isotopes separation by the laser assisted retarded condensation (SILARC) method”, Separation and Purification Technology, 176:4 (2017), 402–411 (cited: 12) (cited: 14)
2019
27.
A. N. Pechen’, “Some mathematical problems of control of quantum systems”, Journal of Mathematical Sciences, 241:2 (2019), 185–190 (cited: 1)
28.
N. B. Il’yn, A. N. Pechen’, “Discrete approximations of dynamical quantum Zeno effect”, Journal of Mathematical Sciences, 241:2 (2019), 158–167
2016
29.
A. N. Pechen, “On the speed gradient method for generating unitary quantum operations for closed quantum systems”, Russian Math. Surveys, 71:3 (2016), 597–599 (cited: 3) (cited: 4)
30.
Alexander N. Pechen, Nikolay B. Il'in, “On the problem of maximizing the transition probability in an $n$-level quantum system using nonselective measurements”, Proc. Steklov Inst. Math., 294 (2016), 233–240 (cited: 6) (cited: 3)
31.
A. N. Pechen, N. B. Ilin, “On extrema of the objective functional for short-time generation of single-qubit quantum gates”, Izv. Math., 80:6 (2016), 1200–1212 , arXiv: 1909.12958 (cited: 1)
32.
K. A. Lyakhov, H. J. Lee, A. N. Pechen, “Some features of Boron isotopes separation by the laser-assisted retardation of condensation method in multipass irradiation cell implemented as a resonator”, IEEE Journal of Quantum Electronics, 52:12 (2016), 1400208 , 8 pp. (cited: 4) (cited: 5)
33.
Valentina Markusova, Konstantin Fursov, Aleksandr Pechen, Natalya Ivanova, Sergei Dmitriev, Artëm Oganov i dr., “Kak ukrepit pozitsii rossiiskoi nauki v mire? Itogi onlain-diskussii po voprosam publikatsionnoi aktivnosti”, Elektronnoe izdanie «NAUKA I TEKhNOLOGII ROSSII – STRF.ru», 2016 Kak ukrepit pozitsii rossiiskoi nauki v mire
2015
34.
A. N. Pechen, A. S. Trushechkin, “Measurement-assisted Landau-Zener transitions”, Phys. Rev. A, 91:5 (2015), 052316 , 15 pp., arXiv: 1506.08323 (cited: 1) (cited: 15) (cited: 2) (cited: 17)
35.
A. N. Pechen, N. B. Il'in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times”, Proc. Steklov Inst. Math., 289 (2015), 213–220 (cited: 11) (cited: 2) (cited: 2) (cited: 7)
36.
A. N. Pechen, N. B. Il'in, “On critical points of the objective functional for maximization of qubit observables”, Russian Math. Surveys, 70:4 (2015), 782–784 (cited: 9) (cited: 6)
A. N. Pechen, D. J. Tannor, “Control of quantum transmission is trap-free”, Canadian Journal of Chemistry, 92:2 (2014), 157–159 , arXiv: 1403.5700 (cited: 5) (cited: 6)
40.
A. N. Pechen, N. B. Il'in, “Coherent control of a qubit is trap-free”, Proceedings of the Steklov Institute of Mathematics, 285 (2014), 233–240 , arXiv: 1407.5175 (cited: 8) (cited: 4)
41.
Alexander Pechen, Some topics in dynamics and control of quantum systems(in Russian), Presenter Yana Rozova. In the broadcast «Moscow. Territory of science» on radio station «Echo of Moscow» (broadcast is organized jointly with Department of Science, Industrial Policy and Entrepreneurship of Moscow), May 29, 2014
2013
42.
A.. N.. Pechen, N.. B.. Il'in, “Control of two-level quantum systems by measurements”, Trudy mezhdunarodnoi shkoly-konferentsii “Upravlenie i optimizatsiya negolonomnykh sistem” (Pereslavl Zalesskii, Rossiya, 10-13 iyulya 2013 g.), Universitet g. Pereslavlya, 2013, 49–50
43.
A.N. Pechen, “Recent advances in the analysis of quantum control landscapes”, Trudy mezhdunarodnoi konferentsii “Matematicheskaya teoriya upravleniya i mekhanika” (Suzdal, Rossiya, 5–9 iyulya 2013 g.), MIAN, 2013, 276–277
44.
A. N. Pechen, “Introduction to some topics in modern quantum control”, Trudy mezhdunarodnoi shkoly-konferentsii “Upravlenie i optimizatsiya negolonomnykh sistem” (Pereslavl-Zalesskii, Rossiya, 10–13 iyulya 2013 g.), Universitet goroda Pereslavlya, 2013, 22–24
45.
A. N. Pechen, Nekotorye voprosy dinamiki i upravleniya kvantovymi sistemami, Diss. … dokt. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova Rossiiskoi akademii nauk, Moskva, 2013 , 194 pp. www.mi.ras.ru/dis/ref13/pechen_diss_v2.pdf
X.-J. Feng, A. Pechen, A. Jha, R. Wu, H. Rabitz, “Global optimality of fitness landscapes in evolution”, Chemical Science, 3 (2012), 900–906 , Edge Article (cited: 5) (cited: 5)
48.
A. Pechen, “Quantum measurements as a control resource”, OSA Technical Digest (Berlin, Germany, March 19–21, 2012), Optical Society of America, 2012, QW2A.8 , arXiv: 1508.04249
49.
A. Pechen, N. Il'in, “Trap-free manipulation in the Landau-Zener system”, Phys. Rev. A, 86 (2012), 052117 , 6 pp., arXiv: 1304.1357 (cited: 14) (cited: 17)
50.
A. Pechen, “Incoherent light as a control resource”, OSA Technical digest (Berlin, Germany, March 19–21, 2012), Optical Society of America, 2012, JT2A.23 , arXiv: 1212.2253
51.
A. N. Pechen, D. J. Tannor, “Quantum control landscape for a Lambda-atom in the vicinity of second-order traps”, Israel Journal of Chemistry, 52:5 (2012), 467–472 , arXiv: 1508.04169 (cited: 7) (cited: 8)
52.
A. N. Pechen, D. J. Tannor, “Pechen and Tannor Reply”, Phys. Rev. Lett., 108 (2012), 198902 , 1 pp. (cited: 17) (cited: 15)
2011
53.
K. W. Moore, A. Pechen, X.-J. Feng, J. Dominy, V. Beltrani, H. Rabitz, “Universal characteristics of chemical synthesis and property optimization”, Chemical Science, 2:3 (2011), 417–424 , Edge Article (cited: 18) (cited: 6) (cited: 18)
54.
A. N. Pechen, D. J. Tannor, “Are there traps in quantum control landscapes?”, Phys. Rev. Lett., 106 (2011), 120402 , 3 pp., This paper has been selected for the Editor's choice section of Science magazine, vol. 332, p. 514 (29 April 2011): “Look Out for Traps”, by Jake S. Yeston, arXiv: 1508.05434 (cited: 49) (cited: 48)
55.
K. W. Moore, A. Pechen, X.-J. Feng, J. Dominy, V.J. Beltrani, H. Rabitz, “Why is chemical synthesis and property optimization easier than expected?”, Physical Chemistry Chemical Physics, 13:21 (2011), 10048–10070 , Perspective article (cited: 37) (cited: 38)
56.
A. N. Pechen, “Some topics in dynamics and control of open quantum systems”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2(23) (2011), 155–161
57.
A. Pechen, “Engineering arbitrary pure and mixed quantum states”, Phys. Rev. A, 84:4 (2011), 042106 , 6 pp., arXiv: 1210.2281 (cited: 16) (cited: 22)
58.
A. Pechen, “Selected topics in dynamics and control of open quantum systems”, P-Adic Numbers, Ultrametric Analysis and Applications, 3:3 (2011), 248–252
59.
A. N. Pechen, “Critical points of objective functions for quantum control problems”, Tambov University Reports, 16:4 (2011), 1146–1148
2014
60.
A. Pechen, H. Rabitz, “Incoherent control of open quantum systems”, Journal of Mathematical Sciences, 199:6 (2014), 695–701 (cited: 1) (cited: 5)
2010
61.
A. Pechen, C. Brif, R. Wu, R. Chakrabarti, H. Rabitz, “General unifying features of controlled quantum phenomena”, Phys. Rev. A, 82 (2010), 030101(R) , 7 pp., arXiv: 1003.3506 (cited: 10) (cited: 12)
62.
A. Pechen, H. Rabitz, “Unified analysis of terminal-time control in classical and quantum systems”, Europhysics Letters, 91 (2010), 60005 , 6 pp., arXiv: 1011.1269 (cited: 10) (cited: 11)
2009
63.
A. Oza, A. Pechen, J. Dominy, V. Beltrani, K. Moore, H. Rabitz, “Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution”, J. Phys. A, 42:20 (2009), 205305 , 22 pp., arXiv: 0905.1149 (cited: 9) (cited: 8)
2008
64.
A. Pechen, D. Prokhorenko, R. Wu, H. Rabitz, “Control landscapes for two-level open quantum systems”, J. Phys. A, 41:4 (2008), 045205 , 18 pp., arXiv: 0710.0604 (cited: 28) (cited: 31)
65.
R. Wu, A. Pechen, H. Rabitz, M. Hsieh, B. Tsou, “Control landscapes for observable preparation with open quantum systems”, J. Math. Phys., 49:2 (2008), 022108 , 12 pp., arXiv: 0708.2119 (cited: 47) (cited: 46)
66.
F. Shuang, M. Zhou, A. Pechen, R. Wu, O. M. Shir, H. Rabitz, “Control of quantum dynamics by optimized measurements”, Phys. Rev. A, 78 (2008), 063422 , 7 pp., arXiv: 0902.2596 (cited: 23) (cited: 23)
67.
D.-Y. Dong, C.-L. Chen, T.-J. Tarn, A. Pechen, H. Rabitz, “Incoherent control of quantum systems with wavefunction controllable subspaces via quantum reinforcement learning”, IEEE Transactions on Systems, Man and Cybernetics — Part B: Cybernetics, 38:4 (2008), 957–962 (cited: 41) (cited: 19) (cited: 51)
68.
D.-Y. Dong, C.-B. Zhang, H. Rabitz, A. Pechen, T.-J. Tarn, “Incoherent control of locally controllable quantum systems”, J. Chem. Phys., 129 (2008), 154103 , 10 pp., arXiv: 0810.3814 (cited: 29) (cited: 35)
69.
A. Pechen, H. Rabitz, “Incoherent quantum control”, Quantum probability and related topics, QP–PQ: Quantum Probab. White Noise Anal., 23, eds. J. Garcia, R. Quezada, S. Sontz, World Scientific, Hackensack, NJ, 2008, 197–211 (cited: 4)
F. Shuang, A. Pechen, T.-S. Ho, H. Rabitz, “Observation-assisted optimal control of quantum dynamics”, J. Chem. Phys., 126 (2007), 134303 , 7 pp., arXiv: quant-ph/0609084 (cited: 32) (cited: 34)
72.
R. Wu, A. Pechen, C. Brif, H. Rabitz, “Controllability of open quantum systems with Kraus-map dynamics”, J. Phys. A, 40:21 (2007), 5681–5693 , arXiv: quant-ph/0611215 (cited: 55) (cited: 34) (cited: 56)
73.
R. Wu, A. Pechen, H. Rabitz, “Control landscapes for observable preparation with open quantum systems”, Proceedings of the 46th IEEE Conference on Decision and Control (New Orleans, LA, USA, 2007), IEEE, 2007, 6365–6369
2006
74.
A. N. Pechen, “The multi-time correlation functions, free white noise, and the generalized Poisson statistics in the low density limit”, J. Math. Phys., 47 (2006), 033507 , 12 pp., arXiv: math-ph/0701055 (cited: 3) (cited: 3)
75.
A. Pechen, H. Rabitz, “Teaching the environment to control quantum systems”, Phys. Rev. A, 73 (2006), 062102 , 6 pp., arXiv: quant-ph/0609097 (cited: 52) (cited: 58)
76.
A. Pechen, N. Il'in, F. Shuang, H. Rabitz, “Quantum control by von Neumann measurements”, Phys. Rev. A, 74 (2006), 052102 , 7 pp., arXiv: quant-ph/0606187 (cited: 71) (cited: 73)
77.
L. Accardi, S. V. Kozyrev, A. N. Pechen, “Coherent quantum control of $\Lambda$-atoms through the stochastic limit”, Quantum information and computing, QP–PQ: Quantum Probab. White Noise Anal., 19, eds. L. Accardi, M. Ohya, N. Watanabe, World Scientific, Hackensack, NJ, 2006, 1–17 , arXiv: quant-ph/0403100
2005
78.
A. N. Pechen, “White noise approach to the low density limit”, Quantum probability and infinite dimensional analysis, QP–PQ: Quantum Probab. White Noise Anal., 18, eds. M. Schürmann, U. Franz, World Scientific, Hackensack, NJ, 2005, 428–447 , arXiv: quant-ph/0607134
2004
79.
A. Pechen, “On an asymptotic expansion in quantum theory”, Math. Notes, 75:3 (2004), 426–429 , arXiv: 1509.00343 (cited: 2)
80.
A. N. Pechen, “Quantum stochastic equation for a test particle interacting with a dilute Bose gas”, J. Math. Phys., 45:1 (2004), 400–417 , arXiv: math-ph/0303020 (cited: 11) (cited: 5) (cited: 8)
81.
A. A. Baranov, A. N. Pechen, and I. V. Volovich, “Space dependence of entangled states and Franson-type EPR experiments”, Mathematical Modelling in Physics, Engineering and Cognitive Science, 10, eds. A. Yu. Khrennikov, Vaxjo University, 2004, 83–91 , arXiv: quant-ph/0203152
82.
A. N. Pechen, Metod stokhasticheskoi asimptotiki v kvantovoi dinamike, Diss. … kand. fiz.-matem. nauk, MIAN, Moskva, 2004 , 106 pp.
2003
83.
L. Accardi, A. Pechen, I. V. Volovich, “A stochastic golden rule and quantum Langevin equation for the low density limit”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6:3 (2003), 431–453 , arXiv: math-ph/0206032 (cited: 17) (cited: 7) (cited: 13)
2002
84.
A. Pechen, I. V. Volovich, “Quantum multipole noise and generalized quantum stochastic equations”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5:4 (2002), 441–464 , arXiv: math-ph/0202046 (cited: 12) (cited: 4) (cited: 9)
85.
L. Accardi, A. Pechen, I. V. Volovich, “Quantum stochastic equation for the low density limit”, J. Phys. A, 35:23 (2002), 4889–4902 , arXiv: quant-ph/0108112 (cited: 15) (cited: 6) (cited: 14)
Uncomputability of quantum control A. N. Pechen International Bogolyubov Conference Problems of Theoretical and Mathematical Physics dedicated to the 110th anniversary of N. N. Bogolyubov's birth September 10, 2019 13:30
Mathematical problems of quantum technologies A. N. Pechen Second International Youth Workshop "Mathematical Methods in the Problems of Quantum Technologies" November 26, 2018 10:00
Some topics in quantum control A. N. Pechen International conference "Quantum information, statistics, probability" with a special session dedicated to A. S. Holevo's 75-th birthday September 12, 2018 17:00
Управление открытыми квантовыми системами A. N. Pechen International youth workshop «Mathematical methods in the problems of quantum technologies» October 9, 2017 10:00
Some topics in quantum control A. N. Pechen Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS October 31, 2013 11:00
Control of open quantum systems A. N. Pechen Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS December 9, 2010 11:00
Mathematics of quantum technologies, Collected papers, Trudy MIAN, 313, ed. A. N. Pechen, I. V. Volovich, G. G. Amosov, A. E. Teretenkov, 2021 http://mi.mathnet.ru/book1832
2021
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