frequency resonance,
algebra of symmetries,
nonlinear commutation relations,
quantum K\"ahlerian forms,
coherent states.
Main publications:
E. M. Novikova, “New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap”, Math. Notes, 109:5 (2021), 777–793
E. M. Novikova, “On calculating the coefficients in the quantum averaging procedure for the Hamiltonian of the resonance harmonic oscillator perturbed by a differential operator with polynomial coefficients”, Russian journal of mathematical physics, 28:3 (2021), 406-410
Math. Notes, 106:6 (2019), 940–956
Math. Notes, 104:6 (2018), 833–847
M. V. Karasev, E. M. Novikova, E. V. Vybornyi, “Bi-states and 2-level systems in rectangular Penning traps”, Russian journal of mathematical physics, 24:4 (2017), 454–464
Math. Notes, 102:6 (2017), 776–786
Math. Notes, 100:6 (2016), 807–819
M. V. Karasev, E. M. Novikova, “Planar Penning trap with combined resonance and top dynamics on quadratic algebra”, Russian journal of mathematical physics, 22:4 (2015), 463–468
M. V. Karasev, E. M. Novikova, “Eigenstates of the quantum Penning–Ioffe nanotrap at resonance”, Theoret. and Math. Phys., 179:3 (2014), 729–746
M. V. Karasev, E. M. Novikova, “Inserted perturbations generating asymptotical integrability”, Math. Notes, 96:6 (2014), 965–970
M. V. Karasev, E. M. Novikova, “Secondary Resonances in Penning Traps. Non-Lie Symmetry Algebras and Quantum States”, Russian journal of mathematical physics, 20:1 (2013), 283-294
O. V. Blagodyreva, M. V. Karasev, E. M. Novikova, “Cubic Algebra and Averaged Hamiltonian for the Resonance 3:(-1) Penning-Ioffe Trap.”, Russian journal of mathematical physics, 19:4 (2012), 441–450
M. V. Karasev, E. M. Novikova, “Algebra and quantum geometry of multifrequency resonance”, Izv. Math., 74:6 (2010), 1155–1204
E. M. Novikova, “Minimal basis of the symmetry algebra for three-frequency resonance”, Russian journal of mathematical physics, 16:4 (2009), 518–528
M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb–Dirac field”, Theoret. and Math. Phys., 142:1 (2005), 109–127
M. V. Karasev, E. M. Novikova, “Algebras with polynomial commutation relations for a quantum particle in electric and magnetic fields”, Quantum Algebras and Poisson Geometry in Mathematical Physics, American Mathematical Society Translations: Series 2, 216, eds. M V. Karasev, AMS, Providence, Rhode Island, 2005, 19–135
M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman–Stark effect in the hydrogen atom”, Theoret. and Math. Phys., 142:3 (2005), 447–469
M. V. Karasev, E. M. Novikova, “Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field”, Theoret. and Math. Phys., 141:3 (2004), 1698–1724
M. V. Karasev, E. M. Novikova, “Nonlinear Commutation Relations: Representations by Point-Supported Operators”, Math. Notes, 72:1 (2002), 48–65
M. V. Karasev, E. M. Novikova, “Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus”, Math. Notes, 70:6 (2001), 779–797
M. V. Karasev, E. M. Novikova, “Coherent transform of the spectral problem and algebras with nonlinear commutation relations”, Journal of Mathematical Sciences, 95:6 (1999), 2703–2798
M. V. Karasev, E. M. Novikova, “Non-Lie permutation relations, coherent states, and quantum embedding”, Coherent Transform, Quantization, and Poisson Geometry, American Mathematical Society Translations: Series 2, 187, eds. M. V. Karasev, AMS, Providence, Rhode Island, 1998, 1–202https://www.ams.org/books/trans2/187/01/trans2187-01.pdf
M. V. Karasev, E. M. Novikova, “Representation of exact and semiclassical eigenfunctions via coherent states. Hydrogen atom in a magnetic field”, Theoret. and Math. Phys., 108:3 (1996), 1119–1159
M. V. Karasev, E. M. Novikova, “Integral representation of eigenfunctions and coherent states for the Zeeman effect”, Quantization, Coherent States, and Complex Structures, eds. J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov, A. Odzijewicz, Springer, New York, NY, 1995, 201–208
M. V. Karasev, E. M. Novikova, “Quadratic Poisson brackets in the Zeeman effect. Irreducible representations and coherent states”, Russian Math. Surveys, 49:5 (1994), 179–180
M. V. Karasev, E. M. Novikova, “Asymptotics of the solution of the Cauchy problem for the one-dimensional Schrödinger equation”, Math. Notes, 51:1 (1992), 100–102
E. M. Novikova, “New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap”, Math. Notes, 109:5 (2021), 777–793
3.
E. M. Novikova, “On calculating the coefficients in the quantum averaging procedure for the Hamiltonian of the resonance harmonic oscillator perturbed by a differential operator with polynomial coefficients”, Russian journal of mathematical physics, 28:3 (2021), 406-410
2019
4.
Math. Notes, 106:6 (2019), 940–956
2018
5.
Math. Notes, 104:6 (2018), 833–847
2017
6.
Math. Notes, 102:6 (2017), 776–786
7.
M. V. Karasev, E. M. Novikova, E. V. Vybornyi, “Bi-states and 2-level systems in rectangular Penning traps”, Russian journal of mathematical physics, 24:4 (2017), 454–464
E. M. Novikova, “Rezonansnaya planarnaya lovushka Penninga s pryamougolnymi elektrodami”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 16:2 (2017), 69–88https://nano-journal.ru/pdf/30_69-88_Novikova.pdf
2016
9.
Math. Notes, 100:6 (2016), 807–819
10.
E. M. Novikova, “Spektralnye klastery planarnoi lovushki Penninga s rezonansnym narusheniem aksialnoi simmetrii.”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 15:2 (2016), 75–98https://nano-journal.ru/pdf/28_75_98_novikova.pdf
2015
11.
M. V. Karasev, E. M. Novikova, “Planar Penning trap with combined resonance and top dynamics on quadratic algebra”, Russian journal of mathematical physics, 22:4 (2015), 463–468
M. V. Karasev, E. M. Novikova, “Ustoichivye dvumernye tory v lovushke Penninga pri kombinirovannom chastotnom rezonanse”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 13:2 (2015), 55-92https://nano-journal.ru/pdf/24_55_92_karasev.pdf
2014
13.
M. V. Karasev, E. M. Novikova, “Eigenstates of the quantum Penning–Ioffe nanotrap at resonance”, Theoret. and Math. Phys., 179:3 (2014), 729–746
14.
M. V. Karasev, E. M. Novikova, “Inserted perturbations generating asymptotical integrability”, Math. Notes, 96:6 (2014), 965–970
M. V. Karasev, E. M. Novikova, “Secondary Resonances in Penning Traps. Non-Lie Symmetry Algebras and Quantum States”, Russian journal of mathematical physics, 20:1 (2013), 283-294
O. V. Blagodyreva, M. V. Karasev, E. M. Novikova, “Integralnoe predstavlenie sobstvennykh sostoyanii 3:(-1) rezonansnoi nanolovushki Penninga”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 9:1 (2013), 5–18https://nano-journal.ru/images/0/0e/6_pdfsam_Nano15.pdf
2012
17.
O. V. Blagodyreva, M. V. Karasev, E. M. Novikova, “Cubic Algebra and Averaged Hamiltonian for the Resonance 3:(-1) Penning-Ioffe Trap.”, Russian journal of mathematical physics, 19:4 (2012), 441–450
E. M. Novikova, “Kogerentnye sostoyaniya kubicheskoi nelievskoi algebry i spektralnaya zadacha dlya atoma vodoroda v rezonansnom effekte Zeemana-Shtarka”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 7:2 (2012), 59–86https://publications.hse.ru/pubs/share/folder/96hbbb6ri5/69573456.pdf
19.
E. M. Novikova, “Analiticheskoe modelirovanie nablyudaemykh i sostoyanii vodorodopodobnogo tsentra. I. Kvadratichnaya algebra”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 7:1 (2012), 107-124https://nano-journal.ru/images/f/f0/108_pdfsam_Nano11.pdf
M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman–Stark effect in the hydrogen atom”, Theoret. and Math. Phys., 142:3 (2005), 447–469
24.
M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb–Dirac field”, Theoret. and Math. Phys., 142:1 (2005), 109–127
25.
M. V. Karasev, E. M. Novikova, “Algebras with polynomial commutation relations for a quantum particle in electric and magnetic fields”, Quantum Algebras and Poisson Geometry in Mathematical Physics, American Mathematical Society Translations: Series 2, 216, eds. M V. Karasev, AMS, Providence, Rhode Island, 2005, 19–135
2004
26.
M. V. Karasev, E. M. Novikova, “Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field”, Theoret. and Math. Phys., 141:3 (2004), 1698–1724
2002
27.
M. V. Karasev, E. M. Novikova, “Nonlinear Commutation Relations: Representations by Point-Supported Operators”, Math. Notes, 72:1 (2002), 48–65
2001
28.
M. V. Karasev, E. M. Novikova, “Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus”, Math. Notes, 70:6 (2001), 779–797
1999
29.
M. V. Karasev, E. M. Novikova, “Coherent transform of the spectral problem and algebras with nonlinear commutation relations”, Journal of Mathematical Sciences, 95:6 (1999), 2703–2798
M. V. Karasev, E. M. Novikova, “Non-Lie permutation relations, coherent states, and quantum embedding”, Coherent Transform, Quantization, and Poisson Geometry, American Mathematical Society Translations: Series 2, 187, eds. M. V. Karasev, AMS, Providence, Rhode Island, 1998, 1–202https://www.ams.org/books/trans2/187/01/trans2187-01.pdf
1996
31.
M. V. Karasev, E. M. Novikova, “Representation of exact and semiclassical eigenfunctions via coherent states. Hydrogen atom in a magnetic field”, Theoret. and Math. Phys., 108:3 (1996), 1119–1159
1995
32.
M. V. Karasev, E. M. Novikova, “Integral representation of eigenfunctions and coherent states for the Zeeman effect”, Quantization, Coherent States, and Complex Structures, eds. J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov, A. Odzijewicz, Springer, New York, NY, 1995, 201–208
M. V. Karasev, E. M. Novikova, “Coherent states over Lagrangian manifolds and the integral representation of wave functions for the problem of a hydrogen atom in a magnetic field”, Joint sessions of the Petrovskii Seminar on Differential Equations and Mathematical Problems of Physics and of the Moscow Mathematical Society (seventeenth session, 24-27 January 1995), Russian Mathematical Surveys, 50, no. 4, 1995, 100
1994
34.
M. V. Karasev, E. M. Novikova, “Quadratic Poisson brackets in the Zeeman effect. Irreducible representations and coherent states”, Russian Math. Surveys, 49:5 (1994), 179–180
1992
35.
M. V. Karasev, E. M. Novikova, “Asymptotics of the solution of the Cauchy problem for the one-dimensional Schrödinger equation”, Math. Notes, 51:1 (1992), 100–102
2023
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