Peter Samuelsson

Sökresultat

• 2025

  Wigner-function formalism for the detection of single microwave pulses in a resonator-coupled double quantum dot

  Zenelaj, D., Samuelsson, P. & Potts, P. P., 2025 mars 24, I: Physical Review Research. 7, 1, 17 s., 013305.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Quantum Dot 100%
  • Resonator 100%
  • Photosensor 25%
  • Nonlinear Filtering 25%
  • Energy-Time Uncertainty 25%

• Coherence of an Electronic Two-Level System under Continuous Charge Sensing by a Quantum Dot Detector

  Haldar, S., Munk, M., Havir, H., Khan, W., Lehmann, S., Thelander, C., Dick, K. A., Samuelsson, P., Potts, P. P. & Maisi, V. F., 2025 jan., I: Physical Review Letters. 134, 2, 023601.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Quantum Dot 100%
  • Electron Tunneling 33%

• Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator

  De Sousa, G., Bakhshinezhad, P., Annby-Andersson, B., Samuelsson, P., Potts, P. P. & Jarzynski, C., 2025 jan., I: Physical Review E. 111, 1, 014152.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Harmonic Oscillator 100%
  • Quantum Measurement 50%
  • Quantum Technology 50%
  • Ground State 50%
• 2024

  Thermoelectric cooling of a finite reservoir coupled to a quantum dot

  Matern, S., Moreira, S. V., Samuelsson, P. & Leijnse, M., 2024 nov., I: Physical Review B. 110, 20, 205423.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Thermoelectric Cooling 100%
  • Phonon 25%
  • Electric Contact 25%

• Maxwell's demon across the quantum-to-classical transition

  Annby-Andersson, B., Bhattacharyya, D., Bakhshinezhad, P., Holst, D., De Sousa, G., Jarzynski, C., Samuelsson, P. & Potts, P. P., 2024 okt., I: Physical Review Research. 6, 4, 043216.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Quantum-to-Classical Transition 100%
  • Feedback Control 50%
  • Second Law of Thermodynamics 50%
  • Quantum Control 50%
  • Quantum Technology 50%

• Geometric Symmetry Breaking and Nonlinearity Can Increase Thermoelectric Power

  Fast, J., Lundström, H., Dorsch, S., Samuelson, L., Burke, A., Samuelsson, P. & Linke, H., 2024 sep., I: Physical Review Letters. 133, 11, 116302.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Nonlinearity 100%
  • Thermoelectricity 100%
  • Thermoelectrics 100%
  • Nonlinear Term 33%
  • Energy Barrier 33%

• Steady-state entanglement production in a quantum thermal machine with continuous feedback control

  Francesco Diotallevi, G., Annby-Andersson, B., Samuelsson, P., Tavakoli, A. & Bakhshinezhad, P., 2024 maj 1, I: New Journal of Physics. 26, 5, 053005.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Feedback 100%
  • Environment 100%
  • Steady State 100%
  • Feedback Control 100%
  • Standard 50%

• Microwave power harvesting using resonator-coupled double quantum dot photodiode

  Haldar, S., Zenelaj, D., Potts, P., Havir, H., Lehmann, S., Dick, K., Samuelsson, P. & Maisi, V., 2024 feb. 15, I: Physical Review B. 109, 8, 6 s., L081403.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Microwave 100%
  • Photodiode 100%
  • Quantum Dot 100%
  • Resonator 100%
  • Energy Harvesting 100%
• 2023

  Stochastic Thermodynamics of a Quantum Dot Coupled to a Finite-Size Reservoir

  Moreira, S. V., Samuelsson, P. & Potts, P. P., 2023 dec., I: Physical Review Letters. 131, 22, 220405.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Thermodynamics 100%
  • Quantum Dot 100%
  • Work 100%
  • Temperature 100%
  • Variation 50%

• Quantum dot source-drain transport response at microwave frequencies

  Havir, H., Haldar, S., Khan, W., Lehmann, S., Dick, K. A., Thelander, C., Samuelsson, P. & Maisi, V. F., 2023 nov. 15, I: Physical Review B. 108, 20, 205417.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Experiment 100%
  • Drain 100%
  • Low Frequency 100%
  • Quantum Dot 100%
  • Response 100%

• Photon emission statistics of a driven microwave cavity

  Portugal, P., Brange, F., Kansanen, K. S. U., Samuelsson, P. & Flindt, C., 2023 juli, I: Physical Review Research. 5, 3, 033091.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Microwave 100%
  • Electron 33%
  • Foci 33%
  • Deviation 33%
  • Gaussian Distribution 33%

• Information-to-work conversion in single-molecule experiments: From discrete to continuous feedback

  Schmitt, R. K., Potts, P. P., Linke, H., Johansson, J., Samuelsson, P., Rico-Pasto, M. & Ritort, F., 2023 maj, I: Physical Review E. 107, 5, L052104.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Work 100%
  • Molecules 100%
  • Information 100%
  • Feedback 100%
  • Experiments 100%

• Entanglement and thermokinetic uncertainty relations in coherent mesoscopic transport

  Prech, K., Johansson, P., Nyholm, E., Landi, G. T., Verdozzi, C., Samuelsson, P. & Potts, P. P., 2023 apr., I: Physical Review Research. 5, 2, 023155.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Coherence 100%
  • Model 60%
  • Behavior 40%
  • Technology 20%
  • Correlation 20%
• 2022

  Full counting statistics of the photocurrent through a double quantum dot embedded in a driven microwave resonator

  Zenelaj, D., Potts, P. P. & Samuelsson, P., 2022 nov. 21, I: Physical Review B. 106, 13 s., 205135.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Microwave 100%
  • Photocurrent 100%
  • Resonator 100%
  • Photoelectric Emission 100%
  • Quantum Dot 100%

• Probabilistically violating the first law of thermodynamics in a quantum heat engine

  Kerremans, T., Samuelsson, P. & Potts, P. P., 2022, I: SciPost Physics. 12, 5, 168.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Work 100%
  • First Law of Thermodynamics 100%
  • Thermodynamics 66%
  • Quantum Fluctuation 66%
  • Information 33%

• Quantum Fokker-Planck Master Equation for Continuous Feedback Control

  Annby-Andersson, B., Bakhshinezhad, F., Bhattacharyya, D., De Sousa, G., Jarzynski, C., Samuelsson, P. & Potts, P. P., 2022, I: Physical Review Letters. 129, 5, 050401.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Feedback Control 100%
  • Information 66%
  • Feedback 66%
  • Work 33%
  • Utilization 33%
• 2021

  A superconductor free of quasiparticles for seconds

  Mannila, E. T., Samuelsson, P., Simbierowicz, S., Peltonen, J. T., Vesterinen, V., Grönberg, L., Hassel, J., Maisi, V. F. & Pekola, J. P., 2021 dec. 20, I: Nature Physics.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Quasiparticle 100%
  • Technology 12%
  • Electron 12%
  • Burst 12%
  • Rule 12%

• Readout of Quantum Screening Effects Using a Time-Dependent Probe

  Dashti, N., Acciai, M., Kheradsoud, S., Misiorny, M., Samuelsson, P. & Splettstoesser, J., 2021 dec. 10, I: Physical Review Letters. 127, 24, 246802.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Screening Effect 100%
  • Conductor 100%
  • Screening 100%
  • Energy Engineering 50%
  • Observables 50%

• Efficient and continuous microwave photoconversion in hybrid cavity-semiconductor nanowire double quantum dot diodes

  Khan, W., Potts, P. P., Lehmann, S., Thelander, C., Dick, K. A., Samuelsson, P. & Maisi, V. F., 2021 dec., I: Nature Communications. 12, 1, 5130.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Nanowire 100%
  • Quantum Dot 100%
  • Semiconductor Material 100%
  • Diode 100%
  • Detector 50%
• 2020

  Maxwell's demon in a double quantum dot with continuous charge detection

  Annby-Andersson, B., Samuelsson, P., Maisi, V. F. & Potts, P. P., 2020 apr. 6, I: Physical Review B. 101, 16, 165404.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Work 100%
  • Detection 100%
  • Electron 50%
  • Information 50%
  • Model 25%

• Quantum teleportation of single-electron states

  Olofsson, E., Samuelsson, P., Brunner, N. & Potts, P. P., 2020, I: Physical Review B. 101, 19

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

• Reaching the ultimate energy resolution of a quantum detector

  Karimi, B., Brange, F., Samuelsson, P. & Pekola, J. P., 2020, I: Nature Communications. 11, 1, 367.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Temperature 100%
  • Microwave 66%
  • Bath 66%
  • Electron 33%
  • Gamma Radiation 33%
• 2019

  Power, efficiency and fluctuations in a quantum point contact as steady-state thermoelectric heat engine

  Kheradsoud, S., Dashti, N., Misiorny, M., Potts, P. P., Splettstoesser, J. & Samuelsson, P., 2019 aug. 8, I: Entropy. 21, 8, 777.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Fluctuations 100%
  • Heat Engine 100%
  • Contact Point 100%
  • Steady State 100%
  • Thermodynamics 100%

• Minimal excitation single-particle emitters: Comparison of charge-transport and energy-transport properties

  Dashti, N., Misiorny, M., Kheradsoud, S., Samuelsson, P. & Splettstoesser, J., 2019 juli 3, I: Physical Review B. 100, 3, 035405.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Energy Engineering 100%
  • Charge Transport 100%
  • Energy Transport 100%
  • Particle 100%
  • Temperature 66%

• Autonomous conversion of information to work in quantum dots

  Sánchez, R., Samuelsson, P. & Potts, P. P., 2019, I: Physical Review Research. 1, 3, 033066.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Work 100%
  • Information 100%
  • Detailed balance 100%
  • Variation 66%
  • Symmetry 33%

• Charge-photon transport statistics and short-time correlations in a single quantum dot-resonator system with an arbitrarily large coupling parameter

  Van Den Berg, T. L. & Samuelsson, P., 2019, I: Physical Review B. 100, 3, 035408.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Correlation 100%
  • Parameter 100%
  • Quantum Dot 100%
  • Resonator 100%
  • Electron 37%

• Thermodynamic uncertainty relations including measurement and feedback

  Potts, P. P. & Samuelsson, P., 2019, I: Physical Review E. 100, 5, 052137.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Thermodynamics 100%
  • Experiments 75%
  • Signal-to-Noise Ratio 50%
  • Energy Engineering 25%
  • Observables 25%
• 2018

  Detailed Fluctuation Relation for Arbitrary Measurement and Feedback Schemes

  Potts, P. P. & Samuelsson, P., 2018 nov. 21, I: Physical Review Letters. 121, 21, 210603.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Feedback 100%
  • Variation 100%
  • Standards 100%
  • Continuous Feedback 100%
  • Inequality 100%

• Probing charge- and heat-current noise by frequency-dependent fluctuations in temperature and potential

  Dashti, N., Misiorny, M., Samuelsson, P. & Splettstoesser, J., 2018 aug. 7, I: Physical Review Applied. 10, 2, 024007.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Temperature 100%
  • Reaction Temperature 100%
  • Noise 100%
  • Electron 66%
  • Conductor 66%

• Quantum Szilard Engine with Attractively Interacting Bosons

  Bengtsson, J., Tengstrand, M. N., Wacker, A., Samuelsson, P., Ueda, M., Linke, H. & Reimann, S. M., 2018 mars 9, I: Physical Review Letters. 120, 10, 100601.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

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  Fil

  • Work 100%
  • Boson 100%
  • Information 66%
  • Temperature 33%
  • Many Body Problem 33%
  313 Nedladdningar (Pure)

• Nanoscale quantum calorimetry with electronic temperature fluctuations

  Brange, F., Samuelsson, P., Karimi, B. & Pekola, J. P., 2018, I: Physical Review B - Condensed Matter and Materials Physics. 98, 205414.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Temperature 100%
  • Pulse 100%
  • Heat Measurement 100%
  • Detection 66%
  • Injector 66%
• 2017

  Optimal Quantum Interference Thermoelectric Heat Engine with Edge States

  Samuelsson, P., Kheradsoud, S. & Sothmann, B., 2017 juni 23, I: Physical Review Letters. 118, 25, 256801.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Heat Engine 100%
  • Thermoelectrics 100%
  • Interference 100%
  • Performance 50%
  • Interferometer 50%

• Classical-to-quantum crossover in electron on-demand emission

  Kashcheyevs, V. & Samuelsson, P., 2017 juni 22, I: Physical Review B. 95, 24, 245424.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Electron Particle 100%
  • Electron 100%
  • Engineering Process 20%
  • Quantum Mechanics 20%
  • Reaction Mechanism 20%

• Minimal Entanglement Witness from Electrical Current Correlations

  Brange, F., Malkoc, O. & Samuelsson, P., 2017, I: Physical Review Letters. 118, 036804.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Correlation 100%
  • Electron 100%
  • Conductor 50%
  • Cross Correlation 50%
• 2015

  Energy and temperature fluctuations in the single electron box

  van den Berg, T., Brange, F. & Samuelsson, P., 2015, I: New Journal of Physics. 17, 075012.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Öppen tillgång

  • Energy Engineering 100%
  • Single Electron 100%
  • Electron 100%
  • Temperature 100%
  • Electronics 75%

• Subdecoherence Time Generation and Detection of Orbital Entanglement in Quantum Dots

  Brange, F., Malkoc, O. & Samuelsson, P., 2015, I: Physical Review Letters. 114, 176803.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Generation Time 100%
  • Bell 33%
  • Correlation Detection 33%
  • Electron Orbitals 33%
• 2014

  Experimental verification of reciprocity relations in quantum thermoelectric transport

  Matthews, J., Battista, F., Sanchez, D., Samuelsson, P. & Linke, H., 2014, I: Physical Review B (Condensed Matter and Materials Physics). 90, 16, 165428.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Fil

  • Symmetry 100%
  • Magnetic Field 50%
  • Response 50%
  • Inelastic Scattering 50%
  • Injection 50%
  185 Nedladdningar (Pure)

• Full counting statistics of generic spin entangler with quantum dot-ferromagnet detectors

  Malkoc, O., Bergenfeldt, C. & Samuelsson, P., 2014, I: Europhysics Letters. 105, 4, 47013.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Spin 100%
  • Detection 25%
  • Correlation 25%
  • Electron 25%
  • Information 25%

• Hybrid Microwave-Cavity Heat Engine

  Bergenfeldt, C., Samuelsson, P., Sothmann, B., Flindt, C. & Buettiker, M., 2014, I: Physical Review Letters. 112, 7, 076803.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Heat Engine 100%
  • Conductor 100%
  • Microwave 100%
  • Quantum Dot 66%
  • Carnot Efficiency 50%

• Pump-probe scheme for electron-photon dynamics in hybrid conductor-cavity systems

  van den Berg, T., Bergenfeldt, C. & Samuelsson, P., 2014, I: Physical Review B (Condensed Matter and Materials Physics). 90, 8, 085416.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Electron 100%
  • Conductor 100%
  • Quantum Dot 50%
  • Dephasing 50%
  • Transients 33%
• 2013

  A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach

  Karlström, O., Emary, C., Zedler, P., Pedersen, J., Bergenfeldt, C., Samuelsson, P., Brandes, T. & Wacker, A., 2013, I: Journal of Physics A: Mathematical and Theoretical. 46, 6, 065301.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Fil

  • Equation of Motion 100%
  • Model 50%
  • Electron 50%
  • Approximation 50%
  • Retarding 50%
  288 Nedladdningar (Pure)

• Nonlocal transport properties of nanoscale conductor-microwave cavity systems

  Bergenfeldt, C. & Samuelsson, P., 2013, I: Physical Review B (Condensed Matter and Materials Physics). 87, 19, 195427.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Microwave 100%
  • Conductor 100%
  • Quantum Dot 100%
  • Electron 33%
  • Model 16%

• Quantum Heat Fluctuations of Single-Particle Sources

  Battista, F., Moskalets, M., Albert, M. & Samuelsson, P., 2013, I: Physical Review Letters. 110, 12, 126602.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Fluctuations 100%
  • Particle 100%
  • Energy Engineering 50%
  • Temperature 50%
  • Electronics 50%
• 2012

  Microwave quantum optics and electron transport through a metallic dot strongly coupled to a transmission line cavity

  Bergenfeldt, C. & Samuelsson, P., 2012, I: Physical Review B (Condensed Matter and Materials Physics). 85, 4, 045446.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Fil

  • Quantum Optics 100%
  • Polaron 100%
  • Microwave Transmission 50%
  234 Nedladdningar (Pure)

• Optimal pumping of orbital entanglement with single-particle emitters

  Sherkunov, Y., d'Ambrumenil, N., Samuelsson, P. & Buettiker, M., 2012, I: Physical Review B (Condensed Matter and Materials Physics). 85, 8, 081108.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Fil

  • Bell 100%
  • Electron 50%
  • Pulse 50%
  • Electric Potential 50%
  • Conductor 50%
  183 Nedladdningar (Pure)

• Spectral distribution and wave function of electrons emitted from a single-particle source in the quantum Hall regime

  Battista, F. & Samuelsson, P., 2012, I: Physical Review B (Condensed Matter and Materials Physics). 85, 7, 075428.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Fil

  • Electron 100%
  • Wave Function 100%
  • Conductor 16%
  207 Nedladdningar (Pure)

• Supercurrent and Multiple Andreev Reflections in an InSb Nanowire Josephson Junction

  Nilsson, H., Samuelsson, P., Caroff, P. & Xu, H., 2012, I: Nano Letters. 12, 1, s. 228-233

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Nanowire 100%
  • Devices 50%
  • Temperature 33%
  • Solid 33%
  • Superconducting Material 33%
• 2011

  Canyon of current suppression in an interacting two-level quantum dot

  Karlström, O., Pedersen, J., Samuelsson, P. & Wacker, A., 2011, I: Physical Review B (Condensed Matter and Materials Physics). 83, 20, 205412.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  Fil

  • Retarding 100%
  • Symmetry 28%
  • Temperature 28%
  • Holes (Electron Deficiencies) 28%
  • Coherence 14%
  203 Nedladdningar (Pure)

• Proposal for nonlocal electron-hole turnstile in the quantum Hall regime

  Battista, F. & Samuelsson, P., 2011, I: Physical Review B (Condensed Matter and Materials Physics). 83, 12, 125324.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Cycles 100%
  • Fluctuations 100%
  • Accuracy 50%
  • Broad Range 50%
• 2010

  Multiple Andreev reflections in hybrid multiterminal junctions

  Houzet, M. & Samuelsson, P., 2010, I: Physical Review B (Condensed Matter and Materials Physics). 82, 6, 060517.

  Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

  • Electric Potential 100%
  • Current Voltage Characteristics 100%
  • Lead 50%