We analyze cohomological properties of the Krichever map and use the results to study Weierstrass... more We analyze cohomological properties of the Krichever map and use the results to study Weierstrass cycles in moduli spaces and the tautological ring.
Experimental results recently obtained for Xe(111) are simulated introducing a method which allow... more Experimental results recently obtained for Xe(111) are simulated introducing a method which allows the time-effective simulation of complete non-contact atomic force microscopy (NC-AFM) images for non-reactive surfaces. All features of the experimental image are successfully reproduced. Additionally, the comparison between experiment and simulation allows the maxima in the experimental image to be identified as the actual positions of the xenon
Applied Physics a Solids and Surfaces, May 1, 1988
The photoelectric response of p-n Si photodiodes under pulsed laser illumination (half width 10 n... more The photoelectric response of p-n Si photodiodes under pulsed laser illumination (half width 10 ns) at 532 nm was studied as a function of dose which was varied over 6 orders of magnitude. The photocurrent transients are dominated by a plateau-like feature due to the build up of space charge at the intensities used. Increasing bias voltage increases the height of the plateau and decreases its length. In the low-dose range the length of the transient increases linearly with dose and the collected charge (integrated current) reaches a constant value. At high doses (above 10-5 J/pulse · cm2 or 2.7×1013 quanta/pulse · cm2) considerable charge loss (decrease in quantum yields) is accompanied by a less than proportional increase of the transient lifetime. From model calculations the dose and voltage dependence of the quantum yield of charge collection is shown to be the result of competition between current flow and first and higher order recombination. The model calculations are consistent with experimental results. Rate constants have been obtained by fitting.
Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We ... more Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of projective modules over noncommutative tori (theta-vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. It seems that the theory of theta-vectors should be closely related to Manin's theory of quantized theta-functions, but we don't analyze this relation.
We show that the notions of space and time in algebraic quantum field theory arise from translati... more We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
We show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology ring of moduli... more We show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology ring of moduli space of D-branes without reference to the sl_2 \times sl_2 action. We also give a simple construction of this action.
We define a (kl|q)-dimensional supermanifold as a manifold having q odd coordinates and k + l eve... more We define a (kl|q)-dimensional supermanifold as a manifold having q odd coordinates and k + l even coordinates with l of them taking only nilpotent values. We show that this notion can be used to formulate superconformal field theories with different number of supersymmetries in holomorphic and antiholomorphic sectors.
A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus cor... more A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus corresponds to a constant curvature connection. On a noncommutative toroidal orbifold there is an additional constraint that the connection be equivariant. We study moduli spaces of (equivariant) constant curvature connections on noncommutative even-dimensional tori and on toroidal orbifolds. As an illustration we work out the cases of Z 2 and Z 4 orbifolds in detail. The results we obtain agree with a commutative picture describing systems of branes wrapped on cycles of the torus and branes stuck at exceptional orbifold points.
We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of ... more We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi-Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic cohomology . We discuss a $p$-adic interpretation of the conjecture about integrality of Gopakumar-Vafa invariants.
We consider gauge theories on noncommutative euclidean space . In particular, we discuss the stru... more We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182 .
We study gauge theories on noncommutative tori. It was proved in [5] that Morita equivalence of n... more We study gauge theories on noncommutative tori. It was proved in [5] that Morita equivalence of noncommutative tori leads to a physical equivalence (SO(d, d|Z)-duality) of the corresponding gauge theories. We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the SO(d, d|Z)duality. The relation of our results with those of recent calculations is discussed.
ABSTRACT One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if... more ABSTRACT One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions. The goal of this paper is to study the moduli spaces of quantum curves. We will show how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve). The KP-hierarchy acts on the moduli space of quantum curves; we prove that similarly the discrete KP-hierarchy acts on the moduli space of discrete quantum curves.
We analyze cohomological properties of the Krichever map and use the results to study Weierstrass... more We analyze cohomological properties of the Krichever map and use the results to study Weierstrass cycles in moduli spaces and the tautological ring.
Experimental results recently obtained for Xe(111) are simulated introducing a method which allow... more Experimental results recently obtained for Xe(111) are simulated introducing a method which allows the time-effective simulation of complete non-contact atomic force microscopy (NC-AFM) images for non-reactive surfaces. All features of the experimental image are successfully reproduced. Additionally, the comparison between experiment and simulation allows the maxima in the experimental image to be identified as the actual positions of the xenon
Applied Physics a Solids and Surfaces, May 1, 1988
The photoelectric response of p-n Si photodiodes under pulsed laser illumination (half width 10 n... more The photoelectric response of p-n Si photodiodes under pulsed laser illumination (half width 10 ns) at 532 nm was studied as a function of dose which was varied over 6 orders of magnitude. The photocurrent transients are dominated by a plateau-like feature due to the build up of space charge at the intensities used. Increasing bias voltage increases the height of the plateau and decreases its length. In the low-dose range the length of the transient increases linearly with dose and the collected charge (integrated current) reaches a constant value. At high doses (above 10-5 J/pulse · cm2 or 2.7×1013 quanta/pulse · cm2) considerable charge loss (decrease in quantum yields) is accompanied by a less than proportional increase of the transient lifetime. From model calculations the dose and voltage dependence of the quantum yield of charge collection is shown to be the result of competition between current flow and first and higher order recombination. The model calculations are consistent with experimental results. Rate constants have been obtained by fitting.
Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We ... more Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of projective modules over noncommutative tori (theta-vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. It seems that the theory of theta-vectors should be closely related to Manin's theory of quantized theta-functions, but we don't analyze this relation.
We show that the notions of space and time in algebraic quantum field theory arise from translati... more We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
We show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology ring of moduli... more We show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology ring of moduli space of D-branes without reference to the sl_2 \times sl_2 action. We also give a simple construction of this action.
We define a (kl|q)-dimensional supermanifold as a manifold having q odd coordinates and k + l eve... more We define a (kl|q)-dimensional supermanifold as a manifold having q odd coordinates and k + l even coordinates with l of them taking only nilpotent values. We show that this notion can be used to formulate superconformal field theories with different number of supersymmetries in holomorphic and antiholomorphic sectors.
A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus cor... more A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus corresponds to a constant curvature connection. On a noncommutative toroidal orbifold there is an additional constraint that the connection be equivariant. We study moduli spaces of (equivariant) constant curvature connections on noncommutative even-dimensional tori and on toroidal orbifolds. As an illustration we work out the cases of Z 2 and Z 4 orbifolds in detail. The results we obtain agree with a commutative picture describing systems of branes wrapped on cycles of the torus and branes stuck at exceptional orbifold points.
We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of ... more We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi-Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic cohomology . We discuss a $p$-adic interpretation of the conjecture about integrality of Gopakumar-Vafa invariants.
We consider gauge theories on noncommutative euclidean space . In particular, we discuss the stru... more We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182 .
We study gauge theories on noncommutative tori. It was proved in [5] that Morita equivalence of n... more We study gauge theories on noncommutative tori. It was proved in [5] that Morita equivalence of noncommutative tori leads to a physical equivalence (SO(d, d|Z)-duality) of the corresponding gauge theories. We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the SO(d, d|Z)duality. The relation of our results with those of recent calculations is discussed.
ABSTRACT One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if... more ABSTRACT One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions. The goal of this paper is to study the moduli spaces of quantum curves. We will show how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve). The KP-hierarchy acts on the moduli space of quantum curves; we prove that similarly the discrete KP-hierarchy acts on the moduli space of discrete quantum curves.
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Papers by Albert Schwarz