E-mail: Keywords: 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, 1–202 https://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
