T.Chwiej, S.Bednarek, B.Szafran, J.Adamowski, F.M. Peeters
"Broken one-particle symmetry in few-electron coupled quantum dots "
Phys. Rev. B 73, 075422 (2006)
2005
J. Adamowski, S. Bednarek, B. Szafran
"Phase Transitions in Wigner Molecules"
(eds. B.A. Joyce et al.), Quantum Dots: Fundamentals, Applications, and Frontiers ,
2005 Springer. Printed in Netherlands. 285-299
B. Szafran, F.M. Peeters, S. Bednarek and J. Adamowski
"Exact broken-symmetry states and Hartree.Fock solutions for
quantum dots at high magnetic fields"
Physica E 26, 252-256 (2004)
T. Chwiej, S. Bednarek, J. Adamowski, B. Szafran, F.M. Peeters
"Coulomb-interaction driven anomaly in the Starkeffect for an
exciton in vertically coupled quantum dots.
"
Journal of Luminescence 112 (2005) 122-126
J. Adamowski, A. Kwasniowski and B. Szafran
"
LO-phonon-induced screening of electron.electron
interaction in D. centres and quantum dots.
"
J. Phys.: Condens. Matter 17 (2005) 4489-4500
S. Moskal,S. Bednarek, and J. Adamowski
"
Time-evolution simulation of a controlled-NOT gate with two coupled asymmetric quantum dots
"
Phys. Rev. A 71, 062327
J. Adamowski, S. Bednarek,
and B. Szafran
"
Quantum Computing with Quantum Dots
"
Schedae Informaticae 14 2005 95-111
B. Szafran, T. Chwiej,F. M. Peeters, S. Bednarek, J. Adamowski, and B. Partoens
"
Exciton and negative trion dissociation by an external electric field
in vertically coupled quantum dots
"
Phys. Rev. B 71, 205316 (2005).
B. Szafran, T. Chwiej, F. M. Peeters, S. Bednarek, and J. Adamowski
"
Relative stability of negative and positive trions in model symmetric quantum wires
"
Phys. Rev. B 71, 235305 (2005).
B. Szafran, F.M. Peeters S. Bednarek and J. Adamowski
"In-plane magnetic-field-induced Wigner crystallization in a two-electron quantum dot "
Phys. Rev. B 70, 235335 (2004).
B. Szafran, S. Bednarek, J. Adamowski, M.B. Tavernier, E. Anisimovas and F.M. Peeters
"Accuracy of the Hartree-Fock method for Wigner molecules
at high magnetic fields"
Eur. Phys. J. D 28 (2004) p. 373-380
B. Szafran, F. M. Peeters, S. Bednarek and J. Adamowski
"Anisotropic quantum dots: Correspondence between quantum and classical Wigner molecules,parity symmetry, and broken-symmetry states"
Phys. Rev. B 69 (2004) 125344
T. Prus, B.Szafran, J.Adamowski and S.Bednarek
"A classical model for the magnetic field-induced Wigner crystallization in quantum dots"
J. Phys.: Condens. Matter 16 (2004) 1425
2003
B. Szafran, S. Bednarek, J. Adamowski, M.B. Tavernier, E. Anisimovas and F.M. Peeters
"Accuracy of the Hartree-Fock method for Wigner molecules
at high magnetic fields"
Eur. Phys. J. D 28 (2004) p. 373-380
B. Szafran, F. M. Peeters, S. Bednarek and J. Adamowski
"Anisotropic quantum dots: Correspondence between quantum and classical Wigner molecules,parity symmetry, and broken-symmetry states"
Phys. Rev. B 69 (2004) 125344
B.Szafran, S.Bednarek, T. Chwiej, J.Adamowski
"Electron pars and excitons in quasi-one-dimensional nanostructures."
Acta Physica Polonica 103 (2003) 6
J. Adamowski
"Komputer kwantowy na kropkach kwantowych"
Materiały IV Krajowej Konferencji
"Metody i systemy komputerowe
w badaniach naukowych
i projektowaniu inżynierskim"
Kraków, 26-28 listopada 2003
redakcja: R. Tadeusiewicz, A. Ligęza,
M. Szymkat, s. 1-13
M.B. Tavernier, E. Anisimovas, F.M. Peters, J.Adamowski, S.Bednarek
"Four-electron quantum dot in magnetic field"
Phys. Rev. B 68 (2003) 205305
S.Bednarek ,B.Szafran, K. Lis, J.Adamowski
"Modeling of electronic properties of electrostatic quantum dots"
Phys. Rev. B 68 (2003) 155333
B.Szafran, S.Bednarek, T.Chwiej, J.Adamowski
"Effective interaction for charge carriers confined in quasi-one-dimensional nanostructures"
Phys. Rev. B 68, (2003) 045328
B.Szafran, S.Bednarek, J.Adamowski
"Magnetic-field-induced phase transitions in Wigner molecules"
J. Phys. Condens.Matter 15 (2003) 4189
B.Szafran, S.Bednarek, J.Adamowski
"Magnetic field induced ground
state transitions in Wigner molecules."
Proc. 26-th Int. Conf. On the Physics of
Semiconductors (ed. A.R.Long and J.H.Davies, Institute of Physics Publishing, Bristol, UK) Copyright 2003, CD-ROM D191.
S.Bednarek, T.Chwiej, J.Adamowski, B.Szafran
"Artificial molecules in coupled and single quantum dots
"
Phys. Rev. B 67 (2003) 205316
B.Szafran, P. Sęp, J.Adamowski , S.Bednarek
"Single-electron charging spectra: from natural to artificial atoms"
Physica E 18 (2003) 523
J.Adamowski, S.Bednarek, B.Szafran
"Configuration interaction study of the single-electron transport
in the vertical gated quantum dot"
Phys. Stat. Sol. (b) 237 (2003) 289
B.Szafran, S.Bednarek, J.Adamowski
"Correlation effects in vertical gated quantum dots"
Phys. Rev. B67 (2003) 115323
K.Lis, S.Bednarek, B.Szafran, J.Adamowski
"Electrostatic quantum dots with designed shape of confinement potential."
Physica E 17C (2003) 494
B.Szafran, S.Bednarek,
J.Adamowski
"Magnetic-field-induced transformations of Wigner molecule symmetry in quantum dots"
Phys. Rev. B67 (2003) 045311
S.Bednarek, T.Chwiej, J.Adamowski, B.Szafran
"Correlation in two-electron systems in coupled quantum dots"
Acta Physica Polonica B34 (2003) 637
B.Szafran, S.Bednarek, J.Adamowski
"Magnetic-field induced ground-state transformations in Wigner
molecules"
Proceedings of the 26th International Conference of Physics
of Semiconductor, Edinburgh 2002 jul 29-aug 2, D191.
M.Ciurla, J.Adamowski, B.Szafran, S.Bednarek
"Modelling of confinement potentials in quantum dots"
Physica E 15 (2002) 261-268
B.Szafran, J.Adamowski, S.Bednarek,
"Effect of the repulsive core on the exciton spectrum in a quantum ring"
J. Phys.: Condens. Matter 14 (2002) 73
B.Szafran, S.Bednarek, J.Adamowski,
"Electric- and magnetic-field-induced evolution of transport windows in a vertical quantum dot"
Phys. Rev. B65 (2002) 35316
B.Szafran, B. Stebe, J.Adamowski, S. Bednarek
"Excitonic trions in single and double quantum dots"
Phys. Rev. B66 (2002) 165331
S.Bednarek, B.Szafran, J.Adamowski,
"Theoretical description of electronic properties of vertical gated quantum dots"
Phys. Rev. B64 (2001) 195303
B.Szafran, S.Bednarek, J.Adamowski,
"Parity symmetry and energy spectrum of excitons in coupled self-assembled quantum dots"
Phys. Rev. B64 (2001) 125301
J.Adamowski, S.Bednarek, B.Szafran
"Transport and capacitance spectroscopy of quantum dots"
Acta Phys. Pol. A100 (2001) 145
S.Bednarek, B.Szafran, J.Adamowski
"Induced-charge distribution in vertical quantum dots"
Proceedings of SPIE 4413 (2001) 129
B.Szafran, J.Adamowski, S.Bednarek
"Electron-electron correlation in quantum dots"
Physica E5 (2000) 185
B.Szafran, J.Adamowski, S.Bednarek
"Infrared optical versus transport spectroskopy for few-electron spherical quantum dots"
J. Phys.: Condens. Matter 12 (2000) 6837
S.Bednarek, B.Szafran, J.Adamowski, I.Essaoudi, B.Stebe
"Optical properties of bound polarons in quantum wells"
in "Optical properties of semiconductor nanostructures" (eds. M.L.Sadowski et al.) Kluwer Academic Publishers, the Netherlands, 2000
J.Adamowski, M.Sobkowicz, B.Szafran, S.Bednarek,
"Electron pair in a Gaussian confining potential"
Phys. Rev. B62 (2000) 4234
B.Szafran, J.Adamowski, S.Bednarek
"Few-electron systems in quantum cylinders"
Phys. Rev. B61 (2000) 1971
S.Bednarek, B.Szafran, J.Adamowski
"Solution of the Poisson-Schroedinger problem for a single-electron transistor "
Phys. Rev. B61 (2000) 4461
B.Szafran, B.Stebe, J.Adamowski, S.Bednarek
"Recombination energy for excitonic trions in quantum dots"
J. Phys.: Condens. Matter 12 (2000) 2453
S.Bednarek, B.Szafran, J.Adamowski
"Quantum Coulomb blockade in gate-controlled quantum dots"
Microelec. Eng. 51-52 (2000) 99
B.Szafran, J.Adamowski, S.Bednarek
"Single-electron charging of self assembled quantum dots"
Thin Solid Films 367 (2000) 93
S.Bednarek, B.Szafran, J.Adamowski,
"MBE-grown gate-controlled quantum-dot nanostructure and its current-voltage characteristics"
Thin Solid Films 367 (2000) 97
B.Szafran, S.Bednarek, J.Adamowski
"Theoretical analysis of magnetic-field-induced evolution of transport windows in a vertical quantum dot"
Proc. 25th Int. Conf. Phys. Semicond, Osaka, 2000, p. 1085
B.Szafran, J.Adamowski, S.Bednarek
"Ground and excited states of few-electron systems in spherical quantum dots"
Physica E4 (1999) 1
J.Adamowski, B.Szafran, S.Bednarek, B.Stebe
"Few-electron artificial atoms"
Few-Body Systems Suppl. 10 (1999) 189
S.Bednarek, B.Szafran, J.Adamowski
"Many-electron artificial atoms"
Phys. Rev. B59 (1999) 13036
B.Szafran, B.Stebe, J.Adamowski, S.Bednarek
"Effect of the electron-phonon coupling on the ground state of a D- center in a spherical quantum dot"
Phys. Rev. B60 (1999) 15558
S.Bednarek, B.Szafran, J.Adamowski, I.Essaoudi, B.Stebe
"Phonon resonances in optical spectra of donors in quantum wells"
Physica B273-274 (1999) 947
B.Szafran, S.Bednarek, J.Adamowski
"Theoretical description of shell filling in cylindrical quantum dots"
Acta Phys. Polon. A94 (1998) 555
B.Szafran, J.Adamowski, B.Stebe
"Energy spectrum of D- centres in spherical quantum dots"
J.Phys.: Condens. Matter 10 (1998) 7575
B.Szafran, J.Adamowski, S.Bednarek, B.Stebe
"Formation of bound electron pairs in semiconductor quantum dots"
Molec. Phys. Rep. 21 (1998) 89
S.Bednarek, J.Adamowski
"Metastability and lattice relaxation for D0 and D- donor centers"
Phys. Rev. B57 (1998) 14729
J.M.Shi, F.M.Peeters, G.A.Farias, J.A.K, Freire, G.Q.Hai, J.T.Devreese, S.Bednarek, J.Adamowski
"Polaron effect on D- centers in weakly polar semiconductors"
Phys. Rev. B57 (1998) 3900
B.Szafran, J.Adamowski, S.Bednarek and B.Stebe
"Influence of donor impurity on optical transitions in quantum dots"
Phys. Stat. Sol. B210 (1998) 677
S.Bednarek, J.Adamowski
"Long-range lattice relaxation for donor centers in supercell method"
Mat. Sci. Forum 258-263 (1997) 1287
B.Szafran, J.Adamowski, B.Stebe
"Ground and excited states of D- centres in semiconductor quantum dots"
Mat. Sci. Forum 258-263 (1997) 1707
S.Bednarek, J.Adamowski
"Coexistance of weakly and strongly localized donor states in semiconductors"
Phys. Rev. B55 (1997) 2195
J.Adamowski, B.Spisak
"Two-electron quantum dots in magnetic field"
Acta Phys. Polon. A92 (1997) 695
S.Bednarek, J.Adamowski
"Shallow-level donor states of strong and weak localization"
Proc. of 7th Int. Conf. on Shallow-Level Centers in Semiconductors (eds. C.A.J. Ammerlaan, B. Pajot, World Scientific, Singapore, 1997), p.55
S.Rolnik, J.Adamowski
"Effect of electric and magnetic fields on energy levels of hydrogenic donor in semiconductor quantum wells"
Electron Technology 29 (1996) 100
S.Bednarek, J.Adamowski "Metastable one- and two-electron donor states in GaAs and CdF2" Acta Phys. Polon. A90 (1996) 719
S.Rolnik, J.Adamowski
"Effect of electric and magnetic fields on donor states in semiconductor quantum wells"
Acta Phys. Polon. A90 (1996) 915
S.Bednarek, J.Adamowski
"Long-range lattice deformation for the strongly localized D0 and D- donor centers"
Proc. 23rd Int. Conf. on the Physics of Semiconductors (ed. M.Scheffler, R.Zimmermann, World Scientific, Singapore, 1996), p.2781
S.Bednarek, J.Adamowski
"Effective double-diagonalisation algorithm for quantum-mechanical variational calculations"
Proc. of the 8th Joint EPS-APS Int. Conf. on Physics Computing (eds.P.Borcherds, M.Bubak, A.Maksymowicz, CYFRONET, Krakow, September 17-21, 1996), p.41
M.A.Smondyrev, J.T.Devreese, J.Adamowski
"Adiabatic theory of bipolarons"
Proc. of the VII Int. Conf. on Symmetry Methods in Physics (ed. A.N.Sissakian & G.S.Pogosyan, JINR, Dubna, 1996), Vol.II, p.520
S.Bednarek, J.Adamowski
"Nature of anticrossing between donor energy levels in GaAs" Phys. Rev. B51 (1995) 4687
S.Bednarek, J.Adamowski
"Anion-cation site dependence of pressure coefficients for donors in GaAs"
Acta Phys. Polon. A88 (1995) 671
S.Rolnik, J.Adamowski
"Stark effect for donors in double quantum wells"
Acta Phys. Polon. A88 (1995) 893
S.Rolnik, J.Adamowski
"Stark effect for donors in quantum well"
Proc. 16th Pekar Int. Conf. on the Theory of Semiconductors, Odessa, October 4-7, 1994
[Ukr. Fiz. Zhurn. 40 (1995) 680]
J.Adamowski, M.Bubak
"Ksztalcenie studentow specjalnosci "Fizyka Komputerowa" w Akademii Gorniczo-Hutniczej" Materialy Konferencji
S.Bednarek, J.Adamowski
"Effect of short-range potential and coupling with phonons on impurity states"
Solid State Commun. 91 (1994) 429
J.Adamowski
"Theory of two-electron systems in polar crystals"
"Polarons and Applications", (John Wiley & Sons, Chichester, 1994), pp.183
S.Bednarek, J.Adamowski
"Anticrossing of donor energy levels in GaAs"
Proc. 22nd Int. Conf. on the Physics of Semiconductors (Vancouver, August 15-19, 1994), p.2335
J.Adamowski, M.Bubak
"Ksztalcenie studentow specjalnosci "Fizyka Komputerowa" w Akademii Gorniczo- Hutniczej" Materialy Konferencji "Informatyka na wyzszych uczelniach dla gospodarki narodowej", Gdansk, 17-19.11.1994, s.75
J.Adamowski, S.Bednarek "Stability of large bipolarons" Journal of Physics: Condensed Matter 4 (1992) 2845-2855
S.Bednarek, J.Adamowski "New donor state of s symmetry" Acta Phys. Polon.A 84 (1993) 820-822
1992
S.Bednarek, J.Adamowski "Donor bistability induced by electron-phonon coupling" Materials Science Forum 83-87 (1992) 493-498
1991
S.Bednarek, J.Adamowski "Infrared absorption on shallow donors in CdF2" Acta Phys. Polon.79 (1991) 393-396
S.Bednarek, J.Adamowski "Conduction band influence on the properties of bistable donors" Acta Phys. Polon.80 (1991) 357-360
1990
J.Adamowski "Phonon-induced negative-U properties of donors" Acta Phys. Polon.A 77 (1990) 111-113
S.Bednarek, J.Adamowski "Theoretical description of donor bistability in CdF2" Materials Science Forum 65 & 66 (1990) 427-432
1989
J.Adamowski "Bipolaron localized at the donor center" Acta Phys. Polon.A 75 (1989) 51-53
J.Adamowski "Formation of Frohlich bipolarons" Phys. Rev.B 39 (1989) 3649-3652
J.Adamowski "Properties of D- centers in polar crystals" Phys. Rev.B 39 (1989) 13061-13066
1988
J.Adamowski "Theoretical prediction of the stability of the Frohlich bipolaron" Acta Phys. Polon.A 73 (1988) 345-348
J.Adamowski "Free and localized two-electron systems in polar crystals" Proc. of the 19th Int. Conf. on the Physics of Semiconductors (ed.W.Zawadzki, Institute of Physics, Polish Academy of Sciences, Warszawa, 1988), pp. 1489-1492
J.Adamowski, S.Bednarek "Influence of electron-phonon coupling on the properties of D- centers" Shallow Impurities in Semiconductors 1988 (ed.B.Monemar, Inst.Phys.Conf.Ser. No 95, IOP, Bristol & Philadelphia, 1989) 533-538
S.Bednarek, J.Adamowski "Valence charge distribution around shallow donors in semiconducting compounds" Shallow Impurities in Semiconductors 1988 (ed.B.Monemar, Inst.Phys.Conf.Ser.No 95, IOP, Bristol & Philadelphia, 1989) p.539-544
1986
S.Bednarek, J.Adamowski
"Theory of chemical shift for donors in ZnSe"
Acta Phys. Polon. A69 (1986) 769
J.Adamowski, S.Bednarek
"Properties of energy spectrum for potentials with repulsive core"
Acta Phys. Polon. A68 (1986) 975
J.Adamowski
"Wlasnosci polaronowe kompleksow ekscytonowych w polprzewodnikach"
Zeszyty Naukowe AGH, Nr 1065, Fizyka, Zeszyt 6 (Krakow, 1986)
J.Adamowski
"Degeneracy of energy levels for the superposition of the Coulomb and Yukawa potentials"
Phys. Rev. A33 (1986) 4384
J.Adamowski "Bound eigenstates for the superposition of the Coulomb and Yukawa potentials" Phys. Rev.A 31 (1985) 43-50
J.Adamowski "Energy spectrum of the bound polaron" Phys. Rev.B 32 (1985) 2588-2595
1984
J.Adamowski, B.Gerlach, H.Leschke "General aspects of the functional-integral approach to the polaron and related systems" Polarons and Excitons in Polar Semiconductors and Ionic Crystals (ed.J.T.Devreese & F.Peeters, Plenum Press, New York, 1984) 245-269
J.Adamowski, S.Bednarek "Polaronic versus atomic properties of donors in semiconductors" Proc. of the Int. Conf. EXCITONS'84, Gustrow, 22-26 October, 1984, 227-230
1983
J.Adamowski, B.Gerlach, H.Leschke "Polaronic versus bare excitons: a functional-integration approach to the exciton-phonon problem" Physica 117&118 (1983) 287-289
J.Adamowski, B.Gerlach, H.Leschke "Wegintegral-Methode fur die Exziton-Phonon Wechselwirkung" Wissenschaftiche Zeittschrift, Padagogische Hochschule, Gustrow, 1 (1983) 29-38
J.Adamowski "Energy levels of the bound polaron" Physics of Semiconducting Compounds, Vol.6 (ed.R.R.Galazka & J.Rauluszkiewicz, Ossolineum, Wroclaw, 1983) 139-142
J.E.Dmochowski, J.M.Langer, J.Adamowski "Bound polarons in semiconducting CdF2" Physics of Semiconducting Compounds, Vol.6 (ed.R.R.Galazka & J.Rauluszkiewicz, Ossolineum, Wroclaw, 1983) 147-150
J.Adamowski, S.Bednarek, M.Suffczynski "Binding energy of the biexcitons" Solid State Commun.9 (1971) 2037-2038
1982
J.Adamowski, B.Gerlach, H.Leschke "Explicit evaluation of certain Gaussian functional integrals arising in problems of statistical physics" J.Math.Phys.23 (1982) 243-249
J.Adamowski, S.Bednarek, M.Suffczynski "Exciton-neutral donor complex in polar semiconductors" Physics of Semiconducting Compounds, Vol.4 (ed.J.M.Langer, Ossolineum, Wroclaw, 1982) 139-142
J.Adamowski, S.Bednarek, M.Suffczynski "Binding energy of the biexcitons in isotropic semiconductors" Phil.Mag.26 (1972) 143-151
S.Bednarek, J.Adamowski "Binding energy of four-particle complexes in semiconductors" Phys. Lett.41A (1972) 347-348
1981
J.Adamowski, B.Gerlach, H.Leschke "Treatment of the exciton-phonon interaction via functional integration.I.Harmonic trial actions" Phys. Rev.B 23 (1981) 2943-2950
W.Ungier, M.Suffczynski, J.Adamowski "Properties of excitons bound to neutral donors" Phys. Rev.B 24 (1981) 2109-2114
S.Bednarek, J.Adamowski, M.Suffczynski "Polaron properties of exciton complexes" J.Phys.C 14 (1981) 4405-4414
1980
J.Adamowski, B.Gerlach, H.Leschke
"Feynman's approach to the polaron problem generalized to arbitrary quadratic actions"
Functional Integration: Theory and Applications (ed.J.-P.Antoine & E.Tirapequi, Plenum
Press, New York, 1980), pp.291-301
J.Adamowski, B.Gerlach, H.Leschke
"Strong-coupling limit of polaron energy, revisited"
Phys. Lett.79A (1980) 249-251
1979
W.Ungier, M.Suffczynski, J.Adamowski
"Phonon replicas of bound exciton recombination"
Solid State Electron.21 (1979) 1365-1367
J.Adamowski, S.Bednarek
"Effective exciton-exciton interaction in polar semiconductors"
Solid State Electron.22 (1979) 33-35
J.Adamowski, S.Bednarek, M.Suffczynski
"Binding energy of exciton-neutral donor complexes"
J. Phys. C12 (1979) L325
W.Ungier, M.Suffczynski, J.Adamowski
"Phonon replicas of the recombination of an exciton bound to a neutral donor"
Proc. of the Int. Conf. RECON'79, Prague, 4-7 September, 1979, pp.242
J.Adamowski, S.Bednarek, M.Suffczynski
"Variational wave functions for the biexciton in polar semiconductors"
Solid State Commun. 25 (1978) 89
S.Bednarek, J.Adamowski, M.Suffczynski
"Binding energy of exciton complexes in anisotropic semiconductors"
J.Phys.C 11 (1978) 4515-4522
1977
S.Bednarek, J.Adamowski
"Oddzialywanie efektywne elektronow i dziur w kompleksach ekscytonowych"
Materialy VII Ogolnokrajowego Seminarium Zwiazkow Polprzewodnikowych AII-BVI,
Prace Instytutu Fizyki PAN, Nr 74, (PWN, Warszawa, 1977) 137- 143
J.Adamowski, S.Bednarek
"Wplyw polaryzacji sieci na energie wiazania biekscytonu"
Materialy VII Ogolnokrajowego Seminarium Zwiazkow Polprzewodnikowych AII-BVI,
Prace Instytutu Fizyki PAN, Nr 74, (PWN, Warszawa, 1977) 144-151
S.Bednarek, J.Adamowski, M.Suffczynski
"Effective Hamiltonian for few-particle systems in polar semiconductors"
Solid State Commun.21 (1977) 1-3
1976
J.Adamowski, S.Bednarek, M.Suffczynski
"The influence of the lattice polarization on the biexciton binding energy"
Solid State Commun.20 (1976) 785-787
1972
J. Adamowski, S. Bednarek, M. Suffczynski
"Binding energy of the biexcitons in isotropic semiconductors"
Phil. Mag. 26 (1972) 143-151
S. Bednarek, J. Adamowski
"Binding energy of four-particle complexes in semiconductors"
Phys. Lett. 41A (1972) 347-348
1971
J. Adamowski, S. Bednarek, M. Suffczynski
"Binding energy of the biexcitons"
Solid State Comm. 9 (1971) 2037-2038